AP Physics C: Mechanics FRQ Room
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AP Physics C: Mechanics Free Response Questions
The best way to get better at FRQs is practice. Browse through dozens of practice AP Physics C: Mechanics FRQs to get ready for the big day.
Analysis of a Velocity-Vs-Time Graph
An object’s velocity is recorded along a straight path. The velocity-time graph indicates that the o
Analysis of Experimental Data Table
An experiment on an air track records the displacement of a cart at various times. The data is shown
Analyzing a Parabolic Trajectory
A projectile is launched with an initial speed of 50 m/s at an angle of 45°. Analyze its trajectory
Analyzing a Two-Dimensional Collision
Two objects undergo a collision in a plane. Object A (mass m_A) experiences a force during the colli
Conservation of Energy in Projectile Motion
A projectile is launched from the ground with an initial speed $$v_0 = 50$$ m/s at an angle of $$45°
Designing an Experiment: Motion on an Inclined Air Track
You are asked to design an experiment to determine the coefficient of kinetic friction on an incline
Determination of Acceleration Due to Gravity
A student drops a small metal ball from a 45 m high platform and records its height over time using
Determining Acceleration Due to Gravity from Free Fall
A student conducted an experiment by dropping a metal ball from a height of 45 m. A digital timer co
Determining Instantaneous Acceleration from a Displacement Graph
An experiment recorded the displacement of an object as a function of time using a high-precision se
Determining Velocity from a Position Function with Differentiation Error
An experiment recorded the position of a particle moving along a straight line, modeled by the funct
Distance vs. Displacement Analysis in One-Dimensional Motion
An experiment recorded the motion of a car along a straight road where its distance traveled and dis
Distance vs. Displacement Analysis in One-Dimensional Motion
An object moves along a straight path and its motion is described by the velocity function $$v(t) =
Dynamic Cart on Air Track: Misinterpretation of Frictionless Environment
In an experiment, a dynamic cart was set in motion on an air track to study uniformly accelerated mo
Evaluating an Experimental Claim on Presumed Uniform Acceleration
A media report claims that a series of experiments have shown that objects in free fall experience a
Free Fall Analysis with Terminal Velocity Consideration
A rock is dropped from a cliff 80 meters high. A researcher claims that the measured fall time of th
FRQ 1: Constant Acceleration Experiment
A researcher is investigating the motion of a cart along a frictionless track. The cart, starting fr
FRQ 2: Projectile Motion – Launch Experiment
A researcher uses a projectile launcher to study the flight of a ball launched at an angle. The ball
FRQ 4: Velocity-Time Graph Analysis (EASY)
A velocity versus time graph for an object shows the following behavior: • From $$t=0$$ to $$t=2\,s$
FRQ 6: Motion with Non-Uniform Acceleration
An object experiences a time-dependent acceleration given by $$a(t) = 4*t - 2$$ (in m/s²) and an ini
FRQ 7: Projectile Trajectory Analysis
A projectile is fired from ground level with an initial speed of 50 m/s at an angle of 40° above the
FRQ 15: Circular Motion with Varying Speed
A particle moves along a circular track of radius 5 m with its speed given by $$v(t)= 2 + t$$ (in m/
FRQ 15: Differentiation of a Cubic Displacement Function (EASY)
An object's displacement is given by $$s(t)=3*t^3-5*t^2+2*t$$ (in m). (a) Find the velocity function
FRQ 15: Investigating Uniformly Accelerated Motion Using Integrals
A researcher records the acceleration of an object with a sensor, finding that the acceleration vari
FRQ 19: Analysis of Motion on an Inclined Plane (MEDIUM)
An object slides down a frictionless inclined plane that makes an angle $$\theta$$ with the horizont
Impulse and Momentum with a Variable Force
A cart of mass $$m = 5.0\,kg$$ is subjected to a time-dependent force described by $$F(t)=5*t²$$ (in
Inferring Acceleration from Velocity Data Using Calculus
The following table shows the time and corresponding velocity for an object moving in one dimension,
Integrating an Acceleration Function to Determine Motion
An object's acceleration is described by $$a(t)=6*t-5$$, with initial velocity $$v(0)=2$$ m/s and in
Investigating Motion on an Inclined Plane
A lab experiment was set up to study the motion of a cart on an inclined air track. The cart’s displ
Kinematics with Calculus: Non-Uniform Acceleration
An object moves along the x-axis under a non-uniform acceleration given by $$a(t) = 4*t - 2$$ m/s²,
Lab Investigation: Effects of Launch Angle on Projectile Range
In a controlled laboratory experiment, a student launches a projectile with a fixed initial speed of
Non-linear Position Function Analysis
A particle moves along the x-axis with a non-linear, decaying oscillatory position given by $$x(t)=e
One-Dimensional Uniform Acceleration Analysis
An object moves along a straight line with its position given by $$x(t) = -2*t^3 + 5*t^2 - 3*t + 1$$
Predicting Motion in a Resistive Medium
An object in free fall experiences a time-dependent acceleration given by $$a(t)=g\left(1-\frac{t}{T
Projectile Launch from an Elevated Platform
A ball is launched from a platform 10 meters above the ground with an initial speed of 30 m/s at an
Projectile Motion Experimental Investigation
A student investigates projectile motion using a spring-loaded launcher on an elevated platform. The
Projectile Motion with Drag
Design an experiment to analyze the trajectory of a projectile when including the effects of drag fo
Projectile Motion with Timing Error
In an outdoor lab experiment, a projectile launcher was used to fire a ball at a 45° angle relative
Sinusoidal Position and Velocity Analysis
Consider an object moving in one dimension whose position function is given by $$x(t)=\sin(t)$$, ove
Trajectory Optimization of an Accelerating Car
A car accelerates according to $$a(t)= 6 - 0.5*t$$ (m/s²) with an initial velocity of 10 m/s at $$t=
Variable Acceleration and Integration
An object moves along a line with a time-dependent acceleration given by $$a(t)=6*t - 2$$ (in m/s²).
Variable Acceleration: Analyzing a Non-Uniformly Accelerated Motion
An object moves along a straight path with an acceleration given by $$a(t)=\frac{12}{(t+2)^2}$$ m/s²
Vector Addition in Two-Dimensional Motion
An object is launched with a horizontal velocity of $$30\,m/s$$ and a vertical velocity of $$40\,m/s
Vector Decomposition in Displacement Measurements
A team conducts an experiment where a cart's displacement in two perpendicular directions is given b
Verifying Free Fall Acceleration
Design an experiment to verify the acceleration due to gravity using free-fall motion. Detail your m
Block Under a Varying Force
A 2 kg block moves along a frictionless horizontal surface under the influence of a variable force g
Collision and Energy Loss Analysis
Two objects collide inelastically and stick together. Object A has mass 3 kg moving at 4 m/s, and Ob
Damped Oscillations and Energy Dissipation in a Mass-Spring System
A damped harmonic oscillator with mass m = 2 kg, spring constant k = 50 N/m, and damping coefficient
Elastic Potential Energy in a Spring System
A spring with a spring constant of $$k = 200\,N/m$$ is compressed by 0.25 m from its equilibrium pos
Energy Conservation on a Frictional Ramp with Calculus Approach
A 2-kg block slides down a straight inclined ramp from a height of $$h = 2 \;\text{m}$$. The ramp is
Energy Dissipation due to Friction
A 10 kg block is pushed along a horizontal surface with a coefficient of kinetic friction $$\mu = 0.
Energy Loss Due to Position-Dependent Friction
A block of mass $$m = 5 \;\text{kg}$$ slides along a horizontal surface. The coefficient of kinetic
Equilibrium Points from a Potential Energy Function
A particle of mass 4 kg experiences a potential energy given by $$U(x) = (x - 2)^2 - (2*x - 3)^3$$ (
Experiment on Electric Motor Power Output
Design an experiment to measure the power output of an electric motor used in a small robotic car.
Experimentally Determining the Effect of Angle on Work Done
A crate is pulled over a horizontal surface with a rope, where the angle of the rope with the horizo
Free‐Fall Impact Energy Experiment
In this experiment, a small cart is dropped from a known height and allowed to free-fall until it im
FRQ 5: Assessing the Independence of Power Output from Time Interval
A magazine article claims that two engines delivering the same work are equally powerful, regardless
FRQ 9: Interpreting Drop Test Kinetic and Potential Energy Data
A study provides experimental data for a 3 kg ball dropped from various heights, with the measured s
FRQ 12: Analysis of Cyclist Power Output During a Ride
A cyclist’s performance is monitored by a power meter during a ride. The measured power output over
FRQ 14: Calculus Analysis of Work Done on an Object with a Time-Varying Force
An object with a mass of 3 kg is subjected to a force that varies with time according to the equatio
FRQ 15: Energy Conservation in an Oscillating Spring–Mass System
A 2-kg mass attached to a spring (with spring constant k = 200 N/m) oscillates horizontally. A displ
FRQ 18: Work–Energy Analysis of a Decelerating Elevator
An elevator with a mass of 1200 kg decelerates uniformly as it approaches a floor. A motion analysis
FRQ 19: Analysis of Force–Time Data in a Crash Test
During a crash test, the force experienced by a dummy is recorded as a function of time. The force–t
FRQ 19: Equilibrium Points from a Nonlinear Potential Energy Function
A report presents the nonlinear potential energy function $$U(x) = (x - 2)^2 - (2 * x - 3)^3$$ and c
Horizontal Pulling Work Experiment
A crate is pulled along a horizontal floor by a worker using a rope that makes a constant angle with
Hydraulic Press Work Calculation Experiment
A hydraulic press compresses a metal block. The pressure in the hydraulic fluid varies with displace
Instantaneous Power in a Variable Force Scenario
An object is subjected to a time-dependent force given by $$F(t)=5*t$$ N, and its displacement is de
Potential Energy Curve Analysis
An object of mass 4 kg moves in a potential energy field described by $$U(x) = (x-1)^2 - 0.5*(x-2)^3
Potential Energy Curve of a Diatomic Molecule
The interatomic potential energy of a diatomic molecule can be approximated by the function $$U(r) =
Power Output in Elevator Lifting
A motor lifts an elevator of mass 500 kg at a constant speed of 2.5 m/s over a vertical displacement
Power Output Variation in a Machine
An object is being moved along a straight path by a constant force of 10 N. The displacement as a fu
Relationship Between Force and Potential Energy
For a conservative force, the relationship between force and potential energy is given by $$F(x) = -
Rotational Work and Energy Experiment
A uniform disk with a moment of inertia $$I = 0.5\,kg\cdot m^2$$ is subjected to a variable torque d
Rotational Work-Energy Analysis in a Flywheel
A flywheel with a moment of inertia $$I = 20\,kg\cdot m^2$$ is accelerated from rest to an angular s
Spring Energy Experiment: Measuring Nonlinear Work
A spring exhibits a force-displacement relationship given by $$F(x) = k*x + a*x^3$$, where $$k = 50\
Variable Mass Rocket Energy Analysis
A rocket with an initial mass of 1500 kg expels fuel and decreases its mass linearly to 1200 kg over
Vertical Lift Work Measurement Experiment
In this vertical lift experiment, an object is raised by a motor and its applied force and displacem
Work Done Against Friction on an Inclined Plane
A 5-kg box slides down a 10-m long inclined plane that makes an angle of 30° with the horizontal. Th
Work Done by Friction: Calculus Approach
A 5 kg block slides on a horizontal surface. The coefficient of kinetic friction varies with positio
Work Done in a Resistive Medium
A particle of mass 1 kg moves in a straight line under the influence of two forces: a constant propu
Work-Energy Theorem with Air Resistance
A 0.2-kg ball is thrown vertically upward with an initial speed of $$40 \;\text{m/s}$$. Air resistan
Assessing the Effects of Impact Duration on Impulse
In an experiment, a baseball is struck with varying impact durations. The impulse delivered during e
Astronaut Momentum Conservation
An astronaut with a total mass of 89 kg is floating in space near her shuttle. To reorient herself,
Billiard Ball Collision and Impulse Analysis
In a game of billiards, a moving ball (mass $$0.17\,kg$$, speed $$2\,m/s$$) collides with a stationa
Center of Gravity vs. Center of Mass in a Tilted Rod
A uniform rod is supported on one end by a fulcrum. In an experiment, additional weights were placed
Center of Mass Determination for a Composite L-Shaped Object
Students perform an experiment to determine the center of mass of an L-shaped, composite board. The
Center of Mass of a Composite Object
A composite object is constructed by rigidly attaching two uniform rectangular plates. Plate A has a
Center of Mass of a Non-uniform Rod
Consider a rod of length L = 1 m with a linear density given by $$\lambda(x)=10+6*x$$, where x is me
Center of Mass of a Non-uniform Rod
A thin rod of length 1.0 m has a linear mass density given by $$\lambda(x) = 5 + 3*x$$ (kg/m), where
Center of Mass of a Non-Uniform Rod
A thin rod of length $$0.8$$ m has a linear mass density given by $$\lambda(x) = 5 + 3*x^2$$ (kg/m),
Center of Mass of a Triangular Plate
A thin, homogeneous triangular plate has vertices at (0,0), (4,0), and (0,3) in meters. Determine it
Center of Mass of an L-Shaped Object
An L-shaped object is formed by joining two uniform rods at one end. One rod is horizontal with a le
Center-of-Mass of a Ladder with Varying Linear Density
A ladder of length $$L=2.0\,m$$ has a vertical linear mass density given by $$\lambda(y)=3.0(1+y)$$
Center-of-Mass Shift in an Internal Explosion
Three masses are arranged on a frictionless horizontal surface: m1 = 1 kg at (0,0), m2 = 2 kg at (1,
Complex Rotational and Translational Collision Involving Center of Mass
A uniform rod of length $$2$$ m and mass $$4$$ kg is pivoted frictionlessly about its center. A smal
Composite Body Center of Mass Calculation
A composite system consists of a uniform rectangular block (mass $$5\,kg$$, width $$0.4\,m$$) and a
Conservation of Linear Momentum in a Glider Collision
On a frictionless air track, two gliders collide. The experimental data below list the masses and ve
Damped Harmonic Oscillator Analysis
A mass-spring system subject to damping has its displacement described by the function $$x(t)=0.2\,e
Elastic Collision in Two Dimensions
Two particles collide elastically on a frictionless plane. Particle 1 (mass $$m_1=1.0\,kg$$) initial
Elastic Collision: Two Gliders on an Air Track
Two gliders on an air track experience a head-on elastic collision. Glider X (mass = 1 kg) initially
Explosive Separation and Momentum Conservation
A 2 kg projectile traveling at 15 m/s explodes into two equal fragments (1 kg each). One fragment mo
Fragmentation and Impulse
A stationary explosive device of total mass $$5\,\text{kg}$$ breaks into two fragments. One fragment
FRQ 3: Motion of the Center of Mass under External Force
An object of mass $$10 \ kg$$, initially at rest, is subjected to an external force given by $$F(t)
FRQ 7: Inelastic Collision Analysis
Two carts collide on a frictionless track and stick together. Cart X (mass = 2 kg) moves at +3 m/s a
FRQ 15: Center of Mass versus Center of Gravity
A popular science article claims that for a complex-shaped satellite orbiting Earth, the center of m
Glider Collision on a Frictionless Air Track
Two gliders on an air track are involved in a head-on elastic collision. The data for the gliders is
Impulse and Average Force on a Punted Football
A football (mass = 0.4 kg) is kicked such that its speed increases from 0 to 30 m/s in 8 ms. (a) Use
Impulse and Momentum in Ball Kicking
In an experiment, a soccer player kicks a 0.4 kg ball. A force sensor records the force exerted by t
Impulse Delivered by a Variable Force
A particle experiences a time-dependent force along the x-axis given by $$F(t)=4*t^2 - 12*t + 9$$ N
Impulse from a Time-Varying Force with Graph Stimulus
A force sensor records the force applied to a hockey puck as a function of time while a player strik
Impulse from a Variable Force Graph
A force acting on an object is given by the time-dependent function $$F(t)=200\,\sin\left(\frac{\pi*
Impulse in a Rebounding Ball
A 0.5-kg ball is dropped from a height of 2 m onto a rigid surface. It rebounds with a speed of 1.2
Integrated Analysis of Momentum and Center of Mass in a Multi-Stage Experiment
In a complex experiment, a projectile traveling at 10 m/s with a mass of 5.0 kg breaks apart mid-fli
Momentum Analysis of a Variable Mass Rocket
A rocket in space, free from external gravitational forces, expels fuel continuously. Its mass is gi
Momentum Conservation in a Skaters' Push-Off
Two ice skaters start from rest on frictionless ice. Skater A has a mass of 50 kg and, after pushing
Motion of the Center of Mass under Applied Force
Two blocks, with masses 3 kg and 5 kg, are connected by a massless rope on a frictionless surface. A
Multi-Dimensional Inelastic Collision Analysis
Two particles undergo a perfectly inelastic collision. Particle A (mass = 2 kg) moves with velocity
Multi-object Collision Dynamics
Three carts on a frictionless track collide and stick together. The carts have masses and initial ve
Projectile and Cart Collision: Trajectory Prediction
A 0.2 kg projectile is launched horizontally at 10 m/s from a 20 m high platform. At the same moment
Rocket Propulsion and Center of Mass Dynamics
A rocket has an initial total mass of $$M_0 = 5000\;kg$$ and burns fuel such that its mass decreases
Stability and Center of Mass of a Structure
A T-shaped structure is formed by joining a horizontal rod (mass $$6\,kg$$, length $$2\,m$$) at its
Velocity Determination under a Variable Force
A 2 kg block is pulled on a frictionless surface by a variable force given by $$F(x)=3*x$$ (N) where
Vibrational Motion: Coupled Oscillators
Two masses (m1 = 0.5 kg and m2 = 0.5 kg) are connected by a spring with spring constant k = 200 N/m
Analysis of a Variable Moment of Inertia System
A rotating disk has a moment of inertia that decreases over time as its arms retract, following the
Angular Kinematics on a Rotating Platform
A rotating platform starts from rest and accelerates with a constant angular acceleration $$\alpha$$
Angular Kinematics with Variable Angular Acceleration
A disk rotates with a non-uniform angular acceleration given by $$\alpha(t) = 4*t$$ (in rad/s²). The
Angular Momentum Conservation in Explosive Separation
A symmetric rotating disk of mass $$M$$ and radius $$R$$ is spinning with an angular velocity $$\ome
Angular Momentum Conservation on a Rotating Platform
A child stands on a circular merry-go-round. Initially, the child is at 2.5 m from the center and th
Angular Momentum in Explosive Separation
A spinning disk with an initial angular velocity $$\omega_i$$ undergoes an explosion that breaks it
Application and Critical Review of the Parallel Axis Theorem
A disk of radius $$R$$ and mass $$M$$ has a moment of inertia about its center of mass given by $$I_
Composite Body Rotation
A composite object is formed by welding a solid disk to a thin rod. The disk has mass $$M$$ and radi
Composite Rotational and Translational Dynamics in Rolling Motion
A hoop of mass m and radius R rolls down an inclined plane. Initially, it slides and rolls, so that
Design and Analysis of a Flywheel Energy Storage System
A flywheel, modeled as a solid disk, is used for energy storage. The flywheel has a mass $$M=50 \tex
Designing a Rotational System with Specified Kinetic Energy
A researcher is tasked with designing a rotational system that must store a specified amount of kine
Dynamic Stability of a Rotating Space Station
A rotating space station initially spins with angular velocity $$\omega_i$$ and has a moment of iner
Dynamics of a Rotating System with Friction
A rotating disk with moment of inertia $$I$$ is subject to a frictional torque that is proportional
Experimental Determination of Torsional Oscillations
Design an experiment to measure the torsional oscillation period of a rod suspended by a wire with a
FRQ 3: Application of the Parallel Axis Theorem
A solid disk has a mass M = 10.00 kg and a radius R = 0.50 m. Its moment of inertia about its centra
FRQ 4: Rotational Kinematics of a Disk
A disk starts from rest and rotates with a constant angular acceleration. After t = 4.00 s, the disk
FRQ 17: Moment of Inertia of a Non-Uniform Rod
A rod of length L = 2.00 m has a density that varies with position according to $$\rho(x) = \rho_0 *
Investigation of Angular Acceleration from Experimental Data
In an experiment, the angular displacement (in radians) of a rotating object was recorded at various
Kinetic Energy Redistribution in Rotating Systems
A rotating disk initially has two weights attached at its rim, resulting in a moment of inertia $$I_
Lever Torque Application
A mechanic uses a long lever to lift a heavy object. A force of $$F = 100 \text{ N}$$ is applied at
Net Torque and Angular Acceleration Calculation
A disc with a moment of inertia of 0.5 kg m^2 is acted upon by two tangential forces: 10 N at a radi
Relation Between Linear and Angular Velocity on a Rotating Disk
In an experiment, a rotating disk is used to measure the linear speed of points located at different
Rolling Motion with Transition from Slipping to Pure Rolling
A solid sphere of mass m and radius R is initially sliding and rolling down an inclined plane with a
Rotational Equilibrium Analysis of a Beam
A beam is in static equilibrium under the influence of several forces applied at different distances
Rotational Kinematics: Angular Displacement via Integration
A motor provides an angular acceleration given by $$\alpha(t) = 4 - 0.5*t$$ (in rad/s²) for $$0 \le
Time-dependent Torque and Angular Momentum Change
A disk is subjected to a time-dependent torque described by $$\tau(t) = 10 * \cos(t)$$ N*m. The disk
Time-Resolved Analysis of Angular Acceleration
A wheel's angular velocity is given by $$\omega(t)= 3t^2 + 2t\,rad/s$$. Calculate its angular accele
Torque and Angular Acceleration Relationship
An experiment measures the response of a rotating object to different applied torques. A graph is pl
Torque and the Right-Hand Rule Verification Experiment
Design an experiment to verify the direction of the torque vector as predicted by the right-hand rul
Torsion Pendulum and Restoring Torque Error
In a torsion pendulum experiment, a disk is suspended from a wire and its angular displacement due t
Verification of the Parallel Axis Theorem
A solid disk of mass M = 4 kg and radius R = 0.5 m is considered. The moment of inertia about its ce
Wrench Torque Analysis
A mechanic uses a wrench to loosen a bolt. Consider a wrench of length L = 0.3 m. In part (a), the m
Calculus Approach to Maximum Velocity in SHM
Consider an oscillator whose displacement is given by the sinusoidal function $$y(t) = A \sin(\omega
Calculus of Oscillatory Motion: Velocity and Acceleration
A researcher analyzes the displacement of a mass-spring oscillator given by the function $$y(t) = 0.
Calculus-Based Analysis of Velocity and Acceleration
Consider an oscillator whose displacement is defined by: $$x(t) = 0.1 * \sin(6*t)$$ (a) Differenti
Calculus-Based Prediction of Maximum Speed
A photogate system is set up to record the speed of a mass-spring oscillator. Answer the following p
Comparative Analysis: Spring-Mass System vs. Pendulum Oscillations
A researcher compares the oscillatory behavior of a horizontal spring-mass system with that of a sim
Comparing Sinusoidal and Non-Sinusoidal Oscillatory Motion
In some experiments, the oscillatory motion observed may deviate from a pure sinusoid. Consider a sy
Comparison of SHM in Spring and Pendulum
Compare the simple harmonic motions of a mass-spring oscillator and a simple pendulum (under the sma
Coupled Oscillations in a Two-Mass Spring System
Consider two masses, $$m_1$$ and $$m_2$$, connected by a spring with spring constant $$k$$. Addition
Damped Oscillations in a Spring-Mass System
In an experiment exploring damped oscillations, a block attached to a spring is set oscillating on a
Damped Oscillatory Motion Analysis
A mass-spring system undergoing damped oscillations has a damping force given by \(F_d = - b * v\),
Data Analysis of Damped Oscillations
A damped oscillator is described by the function: $$y(t) = 0.1 * e^{-\frac{b * t}{2m}} * \cos(\omeg
Data Analysis of Oscillatory Motion with Damping Effects
A student report claims that 'damped oscillations follow the exact same simple harmonic law as undam
Dependence of Maximum Speed on Amplitude
For a spring-mass oscillator undergoing simple harmonic motion, analyze how the maximum speed $$v_{m
Deriving Velocity and Acceleration in SHM
A particle oscillates according to the equation $$y(t) = 0.03\sin(12t + \frac{\pi}{4})$$, where \(t\
Determination of Spring Constant via Oscillation Period
An experiment is set up to determine the spring constant k by measuring the period of oscillations f
Determination of the Spring Constant from Experimental Force-Displacement Data
In an experiment to determine the spring constant, a series of force and displacement measurements w
Determining Spring Constant from Experimental Data
An experiment on a spring produced the following data relating displacement $$x$$ (in meters) to for
Determining Spring Constant Through Oscillation Energy Analysis
An experimental report claims that the spring constant k can be precisely determined by equating the
Determining the Phase Constant from Experimental Data
An experiment measuring the displacement of a simple harmonic oscillator produced the following data
Determining the Spring Constant from SHM Measurements
A block of mass $$m$$ is attached to a horizontal spring on a frictionless surface. When displaced f
Differentiating SHM: Velocity and Acceleration
A block attached to a spring oscillates on a frictionless track and its position is recorded by a se
Differentiation in SHM: Velocity and Acceleration
The position of an oscillator is given by the function $$y(t)=0.05 * \sin(10*t+0.3)$$ (with $$y$$ in
Driven Oscillator and Resonance
A forced mass-spring-damper system is subject to an external driving force given by $$F(t) = F_0\sin
Dynamic Equilibrium in a Vertical Oscillator
A researcher studies the oscillatory motion of a block attached to a vertical spring. The block is d
Energy Conservation in a Mass–Spring Oscillator
Examine energy conservation in a mass–spring system and its experimental verification.
Energy Conservation in a Spring Oscillator
A block of mass $$m = 0.2\,kg$$ oscillates horizontally on a frictionless surface attached to a spri
Energy Transformations in a Spring Oscillator
A block attached to a horizontal spring oscillates with amplitude $$A$$. Consider the energy transfo
Energy Transformations in SHM
Consider a block attached to a spring undergoing simple harmonic motion with displacement $$x(t)=A\s
Error Analysis in SHM Measurements
A student conducting an experiment on a mass-spring oscillator records the following period measurem
Evaluating Damped Oscillatory Motion Effects
A mass-spring oscillator with mass $$m = 0.5 \; kg$$, spring constant $$k = 100 \; N/m$$, and dampin
Evaluating Experimental Uncertainties in SHM Measurements
Accurate measurement of the oscillation period is crucial in SHM experiments. In this context, uncer
Experimental Analysis of SHM Data
The displacement data for a mass-spring system were recorded during a laboratory experiment. The fol
Forced Oscillations and Resonance
A mass-spring system is driven by an external force of the form \(F(t) = F_0 \cos(\omega_d t)\) and
FRQ 4: Vertical Motion in a Spring–Block System
A vertical spring–block system is investigated. The equilibrium displacement for different masses at
FRQ 6: Pendulum Motion and the Small Angle Approximation
A simple pendulum is tested for various small angular displacements. The measured periods for oscill
FRQ 10: Differential Equation of a Horizontal Mass-Spring System
Consider a mass attached to a horizontal spring on a frictionless surface. Answer the following:
FRQ 12: Deriving Velocity and Acceleration Functions
Starting with the position function for a simple harmonic oscillator: $$y = A \sin(\omega t + \phi_0
FRQ 13: Determining Angular Frequency from Oscillation Data
An oscillator’s motion is described by $$y = A \sin(\omega t + \phi_0)$$. A set of position measurem
FRQ 19: Vertical Oscillator Dynamics
A mass is attached to a vertical spring. When displaced by a distance $$y$$ from its equilibrium pos
FRQ5: Sinusoidal Description of Oscillatory Motion and Phase Determination
A mass-spring system oscillates with an amplitude of $$A = 0.06\,m$$ and a frequency of $$f = 2.0\,H
FRQ7: Period of a Simple Pendulum under the Small-Angle Approximation
A simple pendulum consists of a mass attached to a massless string of length \(L\). Answer the foll
FRQ17: Calculus-Based Derivation of Velocity and Acceleration in SHM
Consider a mass undergoing simple harmonic motion described by the displacement function: $$x(t)= A
FRQ19: Coupled Oscillators – Normal Modes of a Two-Mass, Three-Spring System
Consider a system in which two identical masses \(m\) are connected in series with three identical s
Impact of Spring Constant Variation on Oscillatory Motion
A researcher studies how varying the spring constant affects the oscillatory motion of a block attac
Mechanical Energy in SHM
A researcher attaches a block of mass $$m = 0.05 \; kg$$ to a horizontal spring with force constant
Oscillation Frequency's Dependence on Mass and Spring Constant
A research claim suggests that 'doubling the mass of an oscillating system will always decrease the
Pendulum Approximation and Small-Angle Motion
A simple pendulum of length $$L$$ oscillates with small amplitude. Using the small-angle approximati
Pendulum Motion: Small-Angle Approximation
A simple pendulum of length $$L = 0.80\,m$$ is released from a small angle. (a) Using the small-angl
Pendulum Oscillations: Small Angle Approximation
A simple pendulum of length $$L=1.5\,\text{m}$$ is set into small-amplitude oscillations. (a) Derive
Pendulum Period and Data Analysis
Explore the period of a simple pendulum and compare experimental data with theoretical predictions.
Period and Frequency Determination
A mass on a spring is observed to take $$0.20\,s$$ to move from its maximum displacement on one side
Spring Force and Energy Analysis
A spring with a force constant $$k = 350 \; N/m$$ and a natural (unstretched) length of 20 cm is str
Stress Testing of Oscillatory Limits
In an advanced experiment, a student increases the amplitude of oscillation for a spring–mass system
Application of Kepler's Second Law to Orbital Motion
Kepler's Second Law states that a line joining a planet and the Sun sweeps out equal areas in equal
Application of Kepler's Third Law
A planet orbits its star in an almost circular orbit with radius a. Use Kepler's Third Law to analyz
Areal Velocity and Angular Momentum in Planetary Motion
A planet of mass $$m$$ orbits a star while conserving its angular momentum $$L$$. Answer the followi
Barycenter Determination in a Sun-Planet Analog with Magnetic Models
A lab experiment simulates the Sun-Earth system using scaled models equipped with magnetic component
Calculating Gravitational Potential in a Non-Uniform Planet
A researcher investigates the gravitational potential inside a planet with a radially varying densit
Calculus Analysis of Gravitational Potential Energy
Gravitational potential energy (GPE) plays a crucial role in systems influenced by gravity. Answer t
Calculus Derivation of Kepler's Second Law
Kepler's Second Law states that a line joining a planet and the Sun sweeps out equal areas during eq
Cannonball Trajectory in a Non-Uniform Gravitational Field
An experiment studies the trajectory of a cannonball launched at a high angle to analyze projectile
Derivation of Gravitational Potential Energy
Starting from Newton's law of gravitation given by $$F(r) = -G * \frac{M * m}{r^2}$$, derive the exp
Derivation of Gravitational Potential Energy Difference
A space probe's gravitational potential energy is given by $$U(r) = -\frac{G M m}{r}$$. Answer the f
Derivation of Kepler's Second Law from Angular Momentum Conservation
Using the principle of conservation of angular momentum, derive Kepler's Second Law which states tha
Derivation of the Virial Theorem for Gravitational Systems
Derive the virial theorem for a gravitationally bound system and apply it to a hypothetical star clu
Deriving Gravitational Potential from Gravitational Force
The gravitational potential \(V(r)\) is related to the gravitational force by calculus. (a) Show th
Designing a Satellite Orbit Experiment
An engineering team is planning an experiment to study satellite orbits around Earth. (a) List the
Designing a Satellite's Stable Orbit
A space agency plans to deploy a satellite into a stable circular orbit around a planet. The gravita
Determination of Gravitational Parameter (GM) from Satellite Orbits
An observational study is undertaken to determine the gravitational parameter (GM) of a planet by an
Determining Gravitational Potential from Force Field Data
An experiment measures the gravitational force as a function of distance, providing data described b
Determining the Gravitational Constant using a Torsion Balance
An experimental apparatus utilizing a torsion balance is used to measure the gravitational forces be
Dynamic Modeling of Planetary Motion in a Binary Star System
Consider a binary star system where two stars of comparable mass orbit their common center of mass i
Eccentricity and Elliptical Orbits
Discuss the role of eccentricity in elliptical orbits and derive the orbit equation in polar coordin
Effects of Non-Spherical Mass Distribution on Satellite Orbits
A planet is not perfectly spherical but exhibits a slight oblateness, introducing a perturbative ter
Energy Conversion in a Gravitational Slingshot Maneuver
A spacecraft performing a gravitational slingshot maneuver around a planet converts gravitational po
Escape Velocity and Energy Conservation
Consider an object of mass m escaping from a planet with mass M, where gravitational potential energ
Examining Relativistic Corrections to Newtonian Gravity
In strong gravitational fields, relativistic corrections become significant compared to Newtonian pr
FRQ 8: Elliptical Orbit – Perihelion and Aphelion Distances
An object travels in an elliptical orbit with a semimajor axis $$a$$ and eccentricity $$e$$. Answer
FRQ 14: Work Done in Changing Orbital Radius
The work done against gravity in changing the orbital radius of an object is computed by integrating
FRQ 16: Graphical Analysis of Gravitational Potential Energy vs. Height
The graph provided shows experimental data for gravitational potential energy (in joules) versus hei
FRQ 18: Non-Uniform Circular Motion in a Varying Gravitational Field
An object in orbit around a planet experiences non-uniform circular motion due to variations in the
FRQ 19: Relativistic Corrections and Perihelion Precession
General relativity provides corrections to Newtonian gravity that can explain the observed perihelio
FRQ 20: Determining the Mass of a Central Body from Satellite Orbits
A satellite is observed to orbit a celestial body with a period $$T$$ and at a radius $$r$$. Using t
Gravitational Energy in a Three-Body System
Consider three point masses m1, m2, and m3 placed at the vertices of a triangle. Analyze the gravita
Gravitational Energy Trade-offs in a Multi-Body System
Examine the experimental data provided for gravitational potential energies between different pairs
Gravitational Interaction between Two Bodies
Consider two masses m1 and m2 separated by a distance r in deep space. Investigate the gravitational
Mathematical Modeling of Tidal Forces
Using the provided data on tidal forces measured at different distances, analyze how the tidal force
Newton vs. Einstein: Conceptual Analysis of Gravity
Compare and contrast Newton's Law of Gravitation with Einstein's theory of General Relativity. Answe
Newtonian Approximation of Gravitational Lensing
Although gravitational lensing is accurately described by General Relativity, a simplified Newtonian
Optimization of Orbital Maneuvers in Multi-Stage Rockets
A multi-stage rocket performs orbital maneuvers to transition from a low Earth orbit to a higher geo
Orbit Stability from Potential Energy Diagrams
Analyze the provided potential energy diagram and determine the regions corresponding to stable and
Orbital Transfer and the Hohmann Maneuver
A spacecraft performs a Hohmann transfer to move from a circular orbit of radius $$r_1$$ to a higher
Pendulum with Variable Amplitude: Nonlinear Oscillation Effects
In this experiment, a simple pendulum is used to study how the oscillation period changes with ampli
Planetary Orbit Analysis via Kepler's Third Law
A researcher is studying the orbits of several planets around a distant star. Observations suggest t
Simulating Satellite Orbital Decay and Atmospheric Drag
An experimental simulation is set up to study the orbital decay of a satellite due to atmospheric dr
Speed Variation in Elliptical Orbits via Angular Momentum Conservation
In an elliptical orbit, a satellite’s speed varies along its path. Using the conservation of angular
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Note Tips from Former AP Students
- Of course, make sure to run through College Board's past FRQ questions!
- Once you’re done with those go through all the questions in the AP Physics C: MechanicsFree Response Room. You can answer the question and have it grade you against the rubric so you know exactly where to improve.
- Reddit it also a great place to find AP free response questions that other students may have access to.