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 $AP Physics C: Mechanics FRQs to get ready for the big day.
Air Resistance and Projectile Motion
In an experiment, two projectiles with different surface textures (one smooth and one rough) are lau
Analysis of Air Resistance Effects on Free Fall
In an experiment on free fall, an object is dropped and its velocity is measured over time. The calc
Analyzing Motion with a Nonlinear Acceleration Function
A particle moves along the x-axis with an acceleration given by $$a(t)=4\cos(t)$$ (m/s²). It has an
Calculus in One-Dimensional Kinematics
Consider an object whose position as a function of time is given by $$x(t)=\sin(t)+t^2$$, where x is
Comparative Analysis of Kinematic Equations
A researcher claims that the kinematic equation $$s=ut+\frac{1}{2}at^2$$ is universally valid for al
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 $$45°
Determining Instantaneous Acceleration from a Displacement Graph
An experiment recorded the displacement of an object as a function of time using a high-precision se
Determining Launch Angle from Experimental Data
A projectile is launched with an unknown initial speed and angle. In an experiment, the total flight
Displacement Calculation from a Velocity-Time Graph
The velocity of an object is depicted by the following graph. Answer the subsequent questions based
Distance vs. Displacement Analysis in One-Dimensional Motion
An object moves along a straight path and its motion is described by the velocity function $$v(t) =
Drone Video Analysis of Free Fall
A drone records a free-falling ball dropped from a 100 m height. Video analysis approximates the bal
Dynamic Motion Analysis: Cubic Position Function
A particle's position along the x-axis is given by $$x(t) = t^3 - 6t^2 + 9t$$ with time t in seconds
Evaluating Non-Uniform Acceleration from Experimental Data
A student records the following velocity data for an object undergoing non-uniform acceleration:
Experimental Determination of g
In a free-fall experiment, a student fits the data to obtain the position function $$h(t)= 4.9*t^2$$
FRQ 3: Projectile Motion with Calculus Analysis (MEDIUM)
A projectile is launched with an initial speed of $$60\,m/s$$ at an angle of $$30^\circ$$ above the
FRQ 5: Calculus-Based Displacement Calculation
An object has a velocity given by the function $$v(t) = 3*t^2 - 2*t + 5$$ (with t in seconds and v i
FRQ 6: Motion on an Inclined Plane
A researcher studies the motion of a block sliding down an inclined plane with friction. The block i
FRQ 9: Piecewise Acceleration Motion (HARD)
An object moves along a straight line with acceleration defined piecewise as follows: For $$0 \le t
FRQ 10: Comparative Analysis of Two Cars with Different Acceleration Profiles
A researcher compares the motion of two cars starting from rest. Car A accelerates at a constant rat
FRQ 10: Experimental Analysis of Free Fall
Below is experimental data from free fall tests for objects dropped from various heights: | Height
FRQ 11: Modeling Motion with Differential Equations
A researcher is modeling the motion of a ski jumper. The dynamics of the jumper's flight can be expr
FRQ 15: Investigating Uniformly Accelerated Motion Using Integrals
A researcher records the acceleration of an object with a sensor, finding that the acceleration vari
FRQ 17: Vector Field Analysis – Wind Impact on Projectile Motion
A researcher examines how a time-varying wind affects the horizontal motion of a projectile. In this
FRQ 19: Analysis of Motion on an Inclined Plane (MEDIUM)
An object slides down a frictionless inclined plane that makes an angle $$\theta$$ with the horizont
FRQ 20: Evaluating Data Uncertainty from a Velocity-Time Graph (EXTREME)
A velocity vs. time graph obtained from an experiment includes error bars on each data point. The be
Graphical Analysis of Distance and Displacement
A student records the position of a runner during a 10-second race, resulting in the following table
Impulse and Momentum with a Variable Force
A cart of mass $$m = 5.0\,kg$$ is subjected to a time-dependent force described by $$F(t)=5*t²$$ (in
Kinematics in a SmartLab Setup: Integration Error
In a SmartLab experiment, sensors measured both the acceleration and displacement of an object movin
Motion in One Dimension: Variable Acceleration
An object moves along the x-axis with an acceleration given by $$a(t) = 3*t$$ (in m/s²). At time $$t
Motion of a Bus on a Curved Track
A bus moves along a curved track with its acceleration given by $$a(t)= 0.2*t + 0.5*\sin(t)$$ (m/s²)
Motion on an Inclined Plane with Friction
A block of mass m slides down an inclined plane making an angle $$\theta$$ with the horizontal. The
Motion with Air Resistance: Approximating Terminal Velocity
A small sphere falling through a medium experiences air resistance proportional to its velocity. Its
One-Dimensional Uniform Acceleration Analysis
An object moves along a straight line with its position given by $$x(t) = -2*t^3 + 5*t^2 - 3*t + 1$$
Pendulum Energy Conservation Experiment
Design an experiment to test the conservation of mechanical energy in a simple pendulum system. Your
Pendulum Motion and Kinematics
A pendulum of length 2 m oscillates with small amplitude. Its angular displacement is given by $$θ(t
Projectile Launch from an Elevated Platform
A ball is launched from a platform 10 meters above the ground with an initial speed of 30 m/s at an
Projectile Motion Analysis
An object is launched with an initial speed of $$60\,m/s$$ at an angle of $$30^\circ$$ above the hor
Projectile Motion using Calculus
A projectile is launched from ground level at an angle of 30° with an initial speed of 40 m/s (negle
Projectile Motion with Air Resistance
Design an experiment to study the effect of launch angle on the horizontal range of a projectile in
Relative Motion: Meeting of Two Objects
Two objects move along a straight line. Object A starts at x = 0 m with a constant velocity of 10 m/
Simultaneous Measurement of Velocity and Acceleration
In an experiment, separate sensors were used to simultaneously measure both the velocity and acceler
Sinusoidal Motion
A particle’s position along the x-axis is given by $$x(t)=8\sin(t)$$, where $$0\leq t\leq2\pi$$ (x i
Skydiver with Air Resistance: Variable Acceleration
A skydiver of mass m experiences air resistance proportional to velocity, characterized by the const
Trajectory Optimization of an Accelerating Car
A car accelerates according to $$a(t)= 6 - 0.5*t$$ (m/s²) with an initial velocity of 10 m/s at $$t=
Uniformly Accelerated Motion on an Inclined Plane
A 5.0-kg block is placed on a 30° inclined plane. When released, it slides down with a coefficient o
Variable Acceleration Analysis
An object experiences variable acceleration described by $$a(t) = 2*t$$ (in m/s²).
Variable Acceleration Analysis Using Calculus
Design an experiment to investigate the motion of an object under a time-varying force that produces
Vector Displacement and Total Distance
An object moves along a straight line in two phases. First, it moves 10 m to the east, then it moves
Verifying Free Fall Acceleration
Design an experiment to verify the acceleration due to gravity using free-fall motion. Detail your m
Work and Energy in Linear Motion
A variable force acts on a 3.0-kg object moving along the x-axis, where the force is given by $$F(x)
Analysis of a Potential Energy Curve
An object of mass 3 kg moves along the x-axis in a potential energy field given by $$U(x) = (x-1)(x-
Block Under a Varying Force
A 2 kg block moves along a frictionless horizontal surface under the influence of a variable force g
Comparative Analysis of Constant and Variable Force Work
Two experiments are performed on a 3 kg object. In Experiment 1, the object is moved under a constan
Comparative Analysis of Constant vs. Variable Gravitational Work
An object of mass $$m= 10 \;\text{kg}$$ is lifted from the ground (assume $$x=0$$) to a height of $$
Comparing Work–Energy Analysis Across Different Reference Levels
A researcher examines the impact of choosing different reference levels for potential energy calcula
Determining Instantaneous Power from a Velocity-Time Graph
A car of mass 1200 kg has its velocity measured as a function of time. The graph provided represents
Elastic Potential Energy and Hooke’s Law
A spring with a spring constant of $$ k = 200 \;N/m $$ is compressed by 0.1 m from its equilibrium p
Energy Analysis in a Damped Spring-Mass Oscillator
A 1 kg mass attached to a spring with spring constant 100 N/m is initially compressed 0.1 m from its
Energy Conservation in a Pendulum
A simple pendulum has a length $$L = 2 \text{ m}$$ and is released from rest at an initial angle of
Energy Conservation in a Pendulum
A simple pendulum of length 2 m and mass 0.5 kg is released from an initial angle of 30° with respec
Energy Loss in Inelastic Collisions Experiment
Two carts on a frictionless track undergo a collision. Cart A (1 kg) moves at 4 m/s and collides wit
Experiment on Electric Motor Power Output
Design an experiment to measure the power output of an electric motor used in a small robotic car.
Experimental Determination of the Coefficient of Friction
A 4 kg block is pulled along a horizontal surface. The applied force, which varies with position, is
Explosive Separation and Energy Distribution
A stationary object of mass $$M = 10\,kg$$ undergoes an explosion and splits into two fragments with
FRQ 1: Vertical Lifting Experiment – Work Calculation
A lab student lifts a 1.5 kg mass vertically at constant velocity and records the force applied alon
FRQ 6: Work Done on a Crate on an Inclined Plane
A 20-kg crate is moved up a 30° inclined plane. Experimental measurements of the force component alo
FRQ 8: Investigation of Variable Power Output in a Pulley System
A pulley system is used to tow a load with a constant force of 100 N. A sensor records the instantan
FRQ 10: Work Done on a Variable Mass System
A recent claim suggests that for systems with variable mass (e.g., rockets), the work done by a non-
FRQ 11: Deriving Force from a Potential Energy Function
A study posits that the force acting on a particle can be obtained via $$F(x) = - \frac{dU}{dx}$$. E
FRQ 15: Energy Conservation in an Oscillating Spring–Mass System
A 2-kg mass attached to a spring (with spring constant k = 200 N/m) oscillates horizontally. A displ
FRQ 16: Evaluating Power Output Measurements in a Rocket Launch
A media report asserts that the power output of a rocket engine can be approximated by the formula $
FRQ 20: Non-Constant Force Work Calculation via Integration
An experiment claims that for a non-constant force, the work done on an object can be accurately com
Impulse and Energy Transfer via Calculus
A 2-kg object experiences a time-dependent force given by $$F(t)= 4*t$$ N for $$0 \leq t \leq 5\,s$$
Investigation of Non-Conservative Forces in a Roller Coaster Model
A researcher develops a model of a roller coaster of mass 500 kg moving along a track with both grav
Kinetic Energy and Work-Energy Theorem Application
A block of mass 2 kg undergoes net work in two different scenarios. Use the work–energy theorem to f
Kinetic Energy Gain in a Roller Coaster Ride
A roller coaster car of mass 500 kg is released from rest at the top of a frictionless hill at a hei
Measuring Work Done against Air Resistance in Free Fall
A researcher studies the motion of a 1 kg object falling under gravity with air resistance. The drag
Potential Energy Curve Analysis
An object of mass m is subject to a potential energy function given by $$U(x) = x^3 - 6*x^2 + 9*x +
Potential Energy Curves and Equilibrium Analysis
An object of mass 4 kg has a potential energy function given by $$U(x) = (x - 2)^2 - (2\,x - 3)^3$$.
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
Pulley System Work–Energy Verification
A two-mass pulley system is used to verify the work–energy theorem. Velocities of both masses are re
Rolling Sphere Energy Experiment
A solid sphere is rolled without slipping down a tilted ramp, and its kinetic energy is measured at
Rotational Work-Energy in a Pulley System
A pulley with a radius of 0.2 m and a moment of inertia $$I = 0.5\,kg\cdot m^2$$ rotates without sli
Runner's Power Output Analysis
In a track experiment, a runner’s power output is calculated using the formula $$P = m*a*v$$ obtaine
Solar Energy Mechanical Conversion Experiment
In a lab setup, a solar panel powers an electric motor that lifts a 10 kg mass vertically by 3 m at
Spectroscopic Potential Energy Curve Analysis
A spectroscopic experiment is conducted to infer the potential energy curve of a diatomic molecule f
Tidal Energy Extraction Analysis
A tidal turbine is installed in a coastal area where water flow speed varies cyclically. The force e
Time-dependent Power and Differential Equations
A machine's power output, $$P(t)$$ in watts, is governed by the differential equation $$\frac{dP}{dt
Variable Gravitational Acceleration Over a Mountain
A hiker lifts a 10 kg backpack up a mountain where the gravitational acceleration decreases linearly
Work and Energy in a Pulley System
A researcher investigates a two-mass system connected by a massless, frictionless pulley. Mass m1 =
Work Done by a Variable Exponential Force
A piston is subjected to a variable force described by $$F(x)=500*\exp(-0.5*x)$$ N, where x is in me
Work Done by a Variable Gravitational Force
An object of mass 2 kg moves from a height of 50 m to 30 m above the Earth's surface. The gravitatio
Work-Energy Principle in a Frictional System
A 5 kg block is moving upward along a 10-degree incline of length 5 m with an initial speed of 7 m/s
Work-Energy Theorem in a Variable Force Field
A particle of mass 2 kg is acted on by a position-dependent force given by $$F(x) = 10 - 2*x$$ N, wh
Work–Energy and Friction: Analyzing a Sliding Block
A researcher investigates the effect of friction on a sliding block. A 4 kg block is launched horizo
Work–Energy Experiment in Varying Potential Fields
A researcher studies the motion of an object of mass 4 kg in a potential energy field described by $
Analysis of an Oblique Collision
Two ice skaters are initially at rest on a frictionless ice surface. They push off each other; skate
Automobile Collision and Impulse Analysis
Two cars are involved in a head-on collision. Car 1 (mass = 1200 kg) is traveling east at 20 m/s, an
Center of Gravity vs. Center of Mass in a Non-Uniform Rod
A vertical rod of length 1.0 m has a linear density given by $$\lambda(x)=5+2*x$$ (kg/m), where x is
Center of Mass Calculation of a Non-Homogeneous Beam
A horizontal beam of length $$4$$ m has a linear mass density given by $$\lambda(x) = 5 + 4 * x^2$$
Center of Mass Determination for a Composite L-Shaped Object
Students perform an experiment to determine the center of mass of an L-shaped, composite board. The
Center of Mass of a Non-uniform Circular Disk
A thin circular disk of radius $$R$$ has a surface mass density given by $$\sigma(\theta)= k\,(1+\co
Center of Mass of a System of Particles in 3D Space
Three point masses are located in 3D space with the following properties: - Mass 1: 2 kg at coordin
Center of Mass of a Variable Density Disk
A circular disk of radius R = 0.5 m has a surface mass density that varies with the radial distance
Center of Mass of a Variable Density Rod
A rod of length $$L = 1\,\text{m}$$ has a linear density given by $$\lambda(x) = 5 + 3*x$$ (in kg/m)
Center of Mass of a Variable Density Two-Dimensional Lamina
Consider a right triangular lamina with a base of length $$b$$ and a height of $$h$$. The density of
Center of Mass of a Variable-Density Rod
Consider a thin rod of length $$L=2.0$$ m with a linear density given by $$\lambda(x)=2+3*x$$ (kg/m)
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
Conservation of Angular Momentum on a Rotating Platform
An ice skater of mass 50 kg spins with arms extended, having a moment of inertia of 3 kg·m² and an a
Conservation of Linear Momentum in Colliding Carts
Two carts on a frictionless track collide. Cart A (mass = 2 kg) moves to the right with a speed of 3
Elastic Collision: Conservation of Momentum and Kinetic Energy
Two spheres A and B collide elastically. Sphere A has a mass of 0.6 kg and an initial velocity of $$
FRQ 8: Center of Mass and Stability
A uniform beam of length $$5 \ m$$ and mass $$50 \ kg$$ is hinged at one end and held horizontally b
FRQ 13: Critical Analysis: Momentum Experiment
A research study investigating momentum transfer in vehicle collisions reports that the measured mom
FRQ 15: Center of Mass versus Center of Gravity
A popular science article claims that for a complex-shaped satellite orbiting Earth, the center of m
Impulse and Average Force on a Punted Football
A football (mass = 0.4 kg) is kicked such that its speed increases from 0 to 30 m/s in 8 ms. (a) Use
Impulse and Center of Mass in a Soccer Kick
A soccer ball (mass $$0.45\,kg$$) initially at rest is kicked, resulting in a launch speed of $$25\,
Impulse in a Variable Gravitational Field
An object of mass 2 kg is thrown vertically upward from the ground with an initial velocity of 50 m/
Impulse-Momentum Theorem with a Non-constant Force
A 0.2 kg hockey puck is struck by a mallet. The force applied by the mallet varies with time and is
Inelastic Collision: Combined Motion
A 0.6 kg ball moving at 4.0 m/s collides head-on with a 0.4 kg ball that is initially at rest. The b
Momentum Analysis of a Variable Mass Rocket
A rocket in space, free from external gravitational forces, expels fuel continuously. Its mass is gi
Momentum Analysis of a Variable-Density Moving Rod
A rod of length $$L=1.5\,m$$ has a linear density function $$\lambda(x)=4+3*x$$ (in kg/m) and is mov
Momentum Change under a Non-Constant Force
A 1.2-kg block on a frictionless surface is subjected to a time-varying force given by $$F(t) = 12*s
Momentum Conservation in Glider Collisions on an Air Track
In a laboratory experiment, students investigate conservation of momentum by allowing two gliders to
Multi-Dimensional Inelastic Collision Analysis
Two particles undergo a perfectly inelastic collision. Particle A (mass = 2 kg) moves with velocity
Multi-Stage Rocket Propulsion using Momentum Conservation
A rocket with an initial total mass of 1000 kg expels propellant at a constant exhaust velocity of $
Oblique Collision of Ice-Hockey Pucks
Two ice-hockey pucks collide on frictionless ice. Puck A (mass = 0.2 kg) moves east at 5 m/s, and Pu
Oscillations: Simple Pendulum Analysis
For a simple pendulum of length 1.5 m undergoing small oscillations, the angular displacement is giv
Ramp Push Experiment: Variable Force Integration
In a laboratory experiment, a cart on a frictionless ramp is pushed by a force that varies with time
Sequential Collisions in One Dimension
A 1-kg cart moving at $$4\,\text{m/s}$$ collides elastically with a stationary 0.5-kg cart. Immediat
Stability Analysis Using Center of Mass on a Pivoted Beam
A uniform beam of length 2.0 m and mass 10 kg is pivoted at one end. A 20 kg mass is suspended from
Stability Analysis: Center of Mass vs. Center of Gravity
A uniform rectangular block of mass 10 kg with dimensions 0.5 m × 0.3 m × 0.2 m rests on a flat surf
Stability and Center of Mass of a Structure
A T-shaped structure is formed by joining a horizontal rod (mass $$6\,kg$$, length $$2\,m$$) at its
Two-Dimensional Elastic Collision Analysis
A 1 kg particle moving horizontally at 4 m/s collides elastically with a 2 kg particle initially at
Vibrational Motion: Coupled Oscillators
Two masses (m1 = 0.5 kg and m2 = 0.5 kg) are connected by a spring with spring constant k = 200 N/m
Analyzing Variable Torque and Angular Acceleration
A rotor with constant moment of inertia $$I = 4 \text{ kg\cdot m}^2$$ is subjected to a time-varying
Angular Impulse Analysis
A flywheel is subjected to a time-dependent torque given by $$\tau(t) = 50 * e^{-2*t}$$ N*m for $$t
Angular Momentum Conservation on a Merry-Go-Round
A child of mass $$m = 30\,kg$$ stands at the edge of a merry-go-round that is modeled as a uniform d
Angular Momentum in a Variable Moment of Inertia System
A researcher examines the dynamics of a rotating system whose moment of inertia changes with time du
Angular Momentum Transfer in a Dual-Wheel System
Two wheels, A and B, are coupled so that friction between them eventually brings them to a common an
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 $$I_
Calculus in Determining the Moment of Inertia of a Continuous Object
A researcher is investigating how non-uniform mass distribution affects the moment of inertia of a t
Calculus-Based Derivation of Torque from Force Distribution
A beam of length $$L$$ is subject to a continuously distributed force. Consider two cases: (i) const
Combined Translational and Rotational Dynamics
A rolling disk collides elastically with a spring, causing the spring to compress before the disk re
Comparative Study of Rotational Kinetic Energy in Different Shapes
Design an experiment to compare the rotational kinetic energy in different shaped objects (for examp
Conservation of Angular Momentum in a Figure Skater's Spin
A figure skater rotates with an initial angular velocity $$\omega_0$$ with her arms extended. When s
Conservation of Angular Momentum in Explosive Separation
A rotating disk of mass $$M = 5.0 \text{ kg}$$ and radius $$R = 0.5 \text{ m}$$, spinning at $$\omeg
Correlation Between Torque and Rotational Energy via Calculus
A student designs an experiment to investigate the relationship between applied torque and rotationa
Differentiating Between Contact and Rolling Without Slip
An experiment is conducted to analyze the motions of objects rolling down an inclined plane. Both th
Dynamics of a Rotating Rod with Sliding Masses
In this advanced experiment, masses are allowed to slide along a horizontal rod attached to a pivot.
Dynamics of a Rotating System with Friction
A rotating disk with moment of inertia $$I$$ is subject to a frictional torque that is proportional
Energy Conservation in Combined Rotational and Translational Motion
A sphere is made to roll down an incline without slipping, converting gravitational potential energy
Energy Conversion in a Rolling Cylinder Experiment
A cylinder rolls without slipping down an inclined plane. The experiment examines how gravitational
Energy Dissipation Due to Friction in a Spinning Disk
A disk is spun up to a high angular velocity and then allowed to slow down due to friction. The expe
FRQ 9: Experimental Determination of Moment of Inertia
A student performs an experiment to determine the moment of inertia of a uniform disk by measuring i
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 *
FRQ 20: Time-Dependent Angular Acceleration with External Torque
A flywheel with moment of inertia \(I = 3.00\,kg\cdot m^2\) experiences an exponentially decaying ex
Impact of Off-Center Mass in Rotational Dynamics
A student attaches a small mass to a rotating disk at a point away from the center to study its effe
Impulse and Angular Momentum: Impact on a Rotating Disk
A solid disk of mass $$M = 2.0 \text{ kg}$$ and radius $$R = 0.25 \text{ m}$$ is spinning with an in
Mass Redistribution and Kinetic Energy in Rotating Systems
In a rotating system, a person on a rotating platform moves closer to the axis, reducing the system’
Rolling Cylinder Down an Incline
A solid cylinder rolls without slipping down an incline. A set of measurements were made at differen
Rolling Motion on an Inclined Plane
A solid cylinder of mass $$M$$ and radius $$R$$ rolls without slipping down an inclined plane from a
Rolling with Slipping Transition
A solid sphere of mass $$M$$ and radius $$R$$ is released from rest on an inclined plane with an ang
Rotational Equilibrium Analysis of a Beam
A beam is in static equilibrium under the influence of several forces applied at different distances
Rotational Inertia of a Non-Uniform Disk
A disk of radius R has a surface mass density given by $$\sigma(r)= \sigma_0 \left(1+\frac{r}{R}\rig
Rotational Kinematics on a Spinning Disk
A rotating disk's angular displacement is measured by the function $$\theta(t) = 0.2\,t^2 + 2\,t$$ (
Torque and Rotational Inertia in Engine Mechanisms
You are exploring the behavior of torque in a small engine. Design an experiment to measure the engi
Torque Equilibrium in a Beam
A horizontal beam is pivoted at one end. On the beam, a force F1 = 100 N is applied 0.8 m from the p
Analyzing the Role of Initial Conditions in SHM
In an experiment on a mass-spring oscillator, students set the system in motion with various initial
Calculus Approach to Maximum Velocity in SHM
Consider an oscillator whose displacement is given by the sinusoidal function $$y(t) = A \sin(\omega
Comparing Vertical and Horizontal Oscillations in Mass-Spring Systems
A claim has been made that 'the behavior of a vertical spring-mass oscillator is identical to that o
Conservation of Mechanical Energy in SHM
A frictionless spring-mass oscillator conserves mechanical energy during its motion. Demonstrate thi
Data Analysis of Oscillatory Motion with Damping Effects
A student report claims that 'damped oscillations follow the exact same simple harmonic law as undam
Deriving Equations for a Damped Harmonic Oscillator
An experiment is designed to study the effects of damping in a spring-mass oscillator. This version
Designing an Experiment on the Inverse Relationship between Mass and Period
A researcher designs an experiment to study the relationship $$T = 2\pi * \sqrt{\frac{m}{k}}$$ in a
Determination of Maximum Elastic Potential Energy
A researcher is examining the energy stored in a spring when it is displaced from its equilibrium po
Determining Maximum Speed from Energy Considerations
An oscillator of mass $$m = 0.1 \; kg$$ is attached to a spring with a spring constant of $$k = 250
Determining Spring Constant from Force-Displacement Data
In a laboratory experiment, the force exerted by a spring is measured for various displacements. The
Differentiating SHM: Velocity and Acceleration
A block attached to a spring oscillates on a frictionless track and its position is recorded by a se
Differentiation in SHM: Velocity and Acceleration
An oscillator is described by the function $$y = A * \sin(\omega * t + \phi_0)$$. Investigate the ve
Dynamic Equilibrium in a Vertical Oscillator
A researcher studies the oscillatory motion of a block attached to a vertical spring. The block is d
Effect of Mass Variation on SHM
A block attached to a spring oscillates, and the period of oscillation is given by $$T = 2\pi\sqrt{\
Elastic Potential Energy and Maximum Speed Calculation
A block of mass $$m = 0.10\,\text{kg}$$ is attached to a spring with a spring constant of $$k = 200\
Energy Conservation in a Spring Oscillator
A block of mass $$m = 0.2\,kg$$ oscillates horizontally on a frictionless surface attached to a spri
Energy Conservation in Pendulum Motion
A pendulum bob of mass $$m=0.5\,\text{kg}$$ is released from rest at an angle of $$20^\circ$$ from t
Energy Exchange in SHM
Consider a mass-spring oscillator with displacement given by: $$x(t) = A * \cos(\omega t)$$, with
Error Analysis in SHM Measurements
A student conducting an experiment on a mass-spring oscillator records the following period measurem
Experimental Analysis of SHM Data
The displacement data for a mass-spring system were recorded during a laboratory experiment. The fol
Experimental Determination of Spring Constant
Utilize experimental data from a mass–spring oscillator to determine the spring constant.
Experimental Verification of Hooke's Law
A physics lab setup involves a horizontal spring-mass system to test Hooke’s law. In this experiment
Fourier Analysis of Oscillation Data
In an advanced experiment, the oscillation of a spring-mass system is recorded and analyzed using Fo
FRQ 6: Sinusoidal Description of SHM
A simple harmonic oscillator has an amplitude of $$A = 3.0\ cm$$ and a frequency of $$f = 4.0\ Hz$$.
FRQ 8: Energy Exchanges in SHM
A graph of elastic potential energy vs. displacement for a spring is provided. Use calculus to deriv
FRQ 9: Effect of Spring Constant on Frequency
For a mass-spring oscillator, the frequency is given by $$f = \frac{1}{2\pi}\sqrt{\frac{k}{m}}$$. An
FRQ 10: Calculus Integration for Work Done in a Spring
Force measurements during the stretching of a spring were recorded as a function of displacement. Us
FRQ 14: Impact of Initial Conditions on SHM
An oscillator is released from an initial displacement of 0.05 m with an initial upward velocity of
FRQ 14: Work Done by a Spring via Integration
Using calculus, derive an expression for the work done in stretching a spring from its natural lengt
FRQ 18: Comparing Oscillatory Systems
Compare the dynamics of a mass-spring system and a simple pendulum. Answer the following:
FRQ1: Hooke’s Law in a Horizontal Spring-Mass System
A horizontal spring with force constant $$k = 250\,N/m$$ is fixed at one end. A block attached to th
FRQ6: Calculus Derivation of Velocity and Acceleration in SHM
For a mass undergoing simple harmonic motion described by the displacement function $$x(t)= A\sin(\o
Lagrangian Mechanics of the Simple Harmonic Oscillator
A researcher employs Lagrangian mechanics to analyze a mass-spring oscillator. Consider a mass $$m$$
Measuring g with a Simple Pendulum
A researcher uses a simple pendulum to measure the acceleration due to gravity. The length of the pe
Oscillations of a Liquid Column in a U-tube
A U-tube containing a liquid with density $$\rho$$ exhibits oscillatory motion when the liquid is di
Oscillatory Motion of a Block on a Horizontal Spring
A block of mass $$m = 0.8 \; kg$$ is attached to a horizontal spring with a spring constant of $$k =
Pendulum Energy Dynamics
Analyze the energy dynamics of a simple pendulum using both theoretical derivations and numerical ca
Pendulum Motion Experimental Analysis
A simple pendulum experiment is used to measure the period of oscillation. A bob is attached to a ma
Pendulum Motion: Small-Angle Approximation
A simple pendulum of length $$L = 0.80\,m$$ is released from a small angle. (a) Using the small-angl
Pendulum Period and Data Analysis
Explore the period of a simple pendulum and compare experimental data with theoretical predictions.
Period Estimation Using Calculus in Simple Pendulum Experiments
An experimental study reports that integrating the motion equations of a simple pendulum leads to pe
SHM with Phase Shift: Initial Conditions Analysis
An oscillator is described by the equation: $$y(t) = A * \sin(2\pi * f * t + \phi)$$ In a particul
Simple Pendulum Energy Analysis
Consider a simple pendulum of length $$L$$ and mass $$m$$ undergoing small oscillations. Answer the
Spring Force and Energy Analysis
A researcher is studying the behavior of a horizontal spring. The spring has a natural length of 12
Spring Force Investigation
A researcher investigates the force exerted by a spring using Hooke's law. The aim is to verify the
Stress Testing of Oscillatory Limits
In an advanced experiment, a student increases the amplitude of oscillation for a spring–mass system
Time-Dependent Analysis of Oscillatory Motion
An oscillator's displacement is given by the function $$x(t)=0.03 * \cos(12*t)$$ (with $$x$$ in mete
Time-Derivative Analysis of Displacement in SHM
An experiment aims to determine the velocity of a mass undergoing simple harmonic motion by calculat
Vertical Mass-Spring Oscillator: Equilibrium and Oscillations
A 2.0-kg mass is attached to the end of a vertical spring with a force constant $$k = 250\,N/m$$. Th
Vertical Oscillations of a Mass-Spring System
A vertical spring with a spring constant of $$k = 150\,\text{N/m}$$ supports a block of mass $$m = 2
Vertical Oscillations on a Spring
A block of mass $$m = 1.5\,kg$$ is attached to a vertical spring with a force constant of $$k = 300\
Vertical Spring–Block Oscillator Dynamics
Investigate the dynamics of a block oscillating vertically on a spring.
Analysis of Orbital Transfer Maneuvers Using Calculus
A spacecraft is initially in a circular orbit of radius $$ r_1 $$ and is to be transferred to a circ
Application of Kepler's Third Law in the Solar System
A table below provides the semi-major axis and orbital period for several planets. Use this data to
Average Orbital Energy and Angular Momentum
For an orbiting satellite, the specific orbital energy and angular momentum are key conserved quanti
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
Comparative Analysis of Gravitational Forces
Using the data provided, compare the gravitational forces between various pairs of celestial bodies.
Comparison of Gravitational and Centripetal Forces
For a satellite in a stable circular orbit, investigate the balance between gravitational and centri
Designing a Cavendish Experiment to Measure the Gravitational Constant
A student plans to design a version of the Cavendish experiment to measure the gravitational constan
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
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
Energy Conservation in Gravitational Fields: Application to Roller Coaster Dynamics
Although gravitational potential energy is most famously applied in celestial mechanics, the concept
Free Fall with Air Resistance: Integral Approach
A free-fall experiment is performed in a laboratory where a sphere is dropped and its position is re
FRQ 3: Center of Mass in the Sun-Earth System
In the Sun-Earth system, although both bodies orbit their common center of mass (barycenter), the di
FRQ 8: Elliptical Orbit – Perihelion and Aphelion Distances
An object travels in an elliptical orbit with a semimajor axis $$a$$ and eccentricity $$e$$. Answer
Gravitational Potential Energy Change for a Satellite
A satellite is moved from a lower orbit to a higher orbit around a planet. Gravitational potential e
Gravitational Potential Energy Differences in Multi-Body Systems
Consider a test mass moving in the gravitational field of two bodies, $$M_1$$ and $$M_2$$. Answer th
Gravitational Potential Energy Measurement on a Roller Coaster
An amusement park ride features a roller coaster that reaches a maximum height of $$50 \;m$$ above t
Gravitational Potential Energy Variations near Earth
An object of mass $$m$$ is elevated in Earth's gravitational field. (a) Derive the expression $$PE =
Gravity Assist in Three-Body Dynamics
In a gravitational slingshot (gravity assist) maneuver, a spacecraft can change its velocity by inte
Investigating Tidal Forces and Differential Gravity Effects
Consider a moon orbiting a planet, where tidal forces arise due to the variation in gravitational fo
Investigating Tidal Forces in a Binary Star System
Tidal forces in binary star systems can have significant effects on the stars’ structures. Answer th
Kepler's Third Law and Satellite Orbits
Using the provided data for satellite orbits, analyze Kepler’s Third Law. Determine the relationship
Newton vs. Einstein: Conceptual Analysis of Gravity
Compare and contrast Newton's Law of Gravitation with Einstein's theory of General Relativity. Answe
Orbit Transfer and Hohmann Transfer Orbits
A spacecraft is transitioning between two circular orbits using a Hohmann transfer orbit. (a) Descri
Orbital Decay Due to Atmospheric Drag
A satellite in low Earth orbit experiences atmospheric drag, resulting in a gradual decrease of its
Orbital Energy Analysis in Elliptical Orbits
The total mechanical energy of a satellite in an elliptical orbit is the sum of its kinetic and grav
Pendulum Orbital Analog and Kepler's Third Law
In a classroom experiment, a simple pendulum is used as an analog to planetary orbits in order to va
Perturbation Analysis of Satellite Orbits
Study the graph showing small deviations from a nominal circular orbit of a satellite. Analyze the p
Predicting Orbital Decay Due to Atmospheric Drag
A low Earth orbit satellite experiences orbital decay due to atmospheric drag. Assume that the drag
Verifying Kepler's Second Law and Angular Momentum Conservation
Kepler’s Second Law states that a line joining a planet and the Sun sweeps out equal areas during eq
Work Done in a Variable Gravitational Field
An object of mass $$m$$ is moved radially from a distance $$r_1$$ to $$r_2$$ in the gravitational fi
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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.