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.
Acceleration from a Given Velocity Function
An object moves along a straight line with its velocity described by $$v(t)= 5*t^2 - 3*t + 2$$ (m/s)
Block on an Inclined Plane: Kinematic Analysis
A block of mass m is released from rest at the top of a frictionless inclined plane of length L = 10
Coupled Motion: Translation and Rotation
A solid cylinder with mass $$m = 2.0$$ kg and radius $$R = 0.5$$ m is released from rest at the top
Determining Motion from a Sine Position Function
An object's position is given by $$x(t)= 3*\sin(t) + t$$ (meters). Analyze its motion using calculus
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
Differential Equation of Motion Under Gravity and Drag
A particle of mass $$m$$ is falling under gravity and experiences a drag force proportional to its v
Displacement and Critical Points for a Time-Dependent Position Function
A particle moves along the x-axis such that its position is given by $$x(t)=4t^2 - t^3$$, where t is
FRQ 1: One‐Dimensional Constant Acceleration
An object moves along a straight line with constant acceleration. Its initial velocity is 5 m/s and
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: Vector Addition and Displacement Analysis
A researcher studies an object moving along a straight path where its motion includes reversals in d
FRQ 6: Relative Motion in Two Dimensions (HARD)
In the xy-plane, two particles have position functions given by: $$\vec{r}_A(t)=(2*t, t^2)$$ and $$\
FRQ 7: Projectile Trajectory Analysis
A projectile is fired from ground level with an initial speed of 50 m/s at an angle of 40° above the
FRQ 11: Air Resistance and Terminal Velocity
An object of mass 2 kg is falling under gravity while experiencing air resistance proportional to it
FRQ 14: Differentiation of a Position Function
An object’s position is given by the function $$x(t)= t^3 - 6*t^2 + 9*t$$ (with x in meters and t in
FRQ 17: Analyzing Motion from a Cubic Position Function
An object’s position is given by $$x(t)= 2*t^3 - 9*t^2 + 4*t$$ (in meters, with time in seconds). An
FRQ 20: Real-World Application – Car Braking Analysis
A car traveling at 30 m/s begins braking uniformly until it comes to a complete stop. Sensors record
Impact Analysis: Collision Avoidance
Two vehicles are moving along a straight road. Vehicle A travels with constant velocity described by
Impulse and Momentum with a Variable Force
A cart of mass $$m = 5.0\,kg$$ is subjected to a time-dependent force described by $$F(t)=5*t²$$ (in
Impulse and Variable Force Analysis
Design an experiment to measure the impulse delivered to a ball by a bat, given that the force varie
Integrating an Acceleration Function to Determine Motion
An object's acceleration is described by $$a(t)=6*t-5$$, with initial velocity $$v(0)=2$$ m/s and in
Investigating Motion on an Inclined Plane
A lab experiment was set up to study the motion of a cart on an inclined air track. The cart’s displ
Motion with Air Resistance: Approximating Terminal Velocity
A small sphere falling through a medium experiences air resistance proportional to its velocity. Its
Newton's Second Law and Force Measurement on a Cart
Design an experiment using a cart on a frictionless track with a pulley system to verify Newton's se
Non-Uniform Acceleration Analysis
A particle's position is given by $$x(t)=\sin(t)-0.5*t^2$$. Analyze its motion using calculus.
Piecewise Motion Analysis
An object moves along a straight line with acceleration defined piecewise as follows: for $$0 \le t
Polynomial Position Function Analysis
A particle’s position along the x-axis is given by the function $$x(t)=t^3 - 6*t^2 + 9*t$$ (in meter
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 on Level Ground
An object is launched from ground level at a 45° angle with an initial speed of 30 m/s (neglect air
Projectile Motion with Air Resistance
Design an experiment to study the effect of launch angle on the horizontal range of a projectile in
Projectile Motion with Calculus Integration
An object is launched from ground level with an initial speed of 50 m/s at an angle of 40° above the
Projectile Motion: Maximum Height and Range
An object is launched from ground level at an angle of 30° above the horizontal with an initial spee
Projectile Range Analysis with Angular Misinterpretation
An experiment was conducted to analyze the range of a projectile launched at various angles. A fixed
Relative Motion Experiment
Two carts on parallel tracks move in the same direction with positions given by $$x_A(t)=5*t$$ and $
Relative Motion in Two Dimensions
A boat is moving eastward relative to the water at 5 m/s. The river current flows southward at 3 m/s
Simple Harmonic Motion in a Spring-Mass System
Design an experiment to investigate simple harmonic motion (SHM) using a spring-mass system. Describ
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
Variable Acceleration Analysis Using Calculus
Design an experiment to investigate the motion of an object under a time-varying force that produces
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 Net Force Experiment
A cart on a frictionless track is subjected to a variable net force given by $$F(t)= 10*t$$ (N). The
Analysis of Mechanical Advantage and Work in a Lever System
A lever is used to lift a 500 N weight. The operator applies a force that varies with the angle, giv
Conservation of Mechanical Energy with Dissipative Forces
A 1 kg ball is dropped from a height of 20 m. Experimental measurements indicate that air resistance
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
Energy Dissipation in a Bouncing Ball
A ball of mass 0.2 kg is dropped from a height of 2 m and rebounds to a height of 1.5 m. Assume that
Energy Dissipation in Damped Oscillations
A damped harmonic oscillator consists of a 1 kg mass attached to a spring (k = 50 N/m) with a dampin
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
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 Energy Loss in Frictional Systems
Design an experiment to investigate the relationship between surface roughness and energy loss durin
FRQ 11: Analysis of a Bungee Jump – Variable Net Force
A bungee jumper with a mass of 70 kg experiences a net force that changes as a function of vertical
Gravitational Potential Energy and Free Fall
A 60-kg acrobat climbs to the top of a 50-m tall platform and then jumps off. Neglecting air resista
Hydraulic Press Work Calculation Experiment
A hydraulic press compresses a metal block. The pressure in the hydraulic fluid varies with displace
Impulse and Energy Transfer via Calculus
A 2-kg object experiences a time-dependent force given by $$F(t)= 4*t$$ N for $$0 \leq t \leq 5\,s$$
Inclined Plane Friction Variation Experiment
A block is allowed to slide down an inclined plane over which the coefficient of friction is not con
Inelastic Collision and Energy Dissipation
Two blocks undergo a perfectly inelastic collision. A 3 kg block moving at 5 m/s collides with a 2 k
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 Change Under a Variable Force
A 2-kg object is subjected to a variable force along a horizontal path given by $$F(x)= 4 + 0.2*x \;
Kinetic Energy Measurement in a Projectile Experiment
A researcher is studying the change in kinetic energy of a small projectile. A ball of mass $$m = 0.
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 and Efficiency in a Wind Turbine
A wind turbine with a rotor radius of 40 m extracts energy from wind. The wind speed varies with hei
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
Projectile Energy Analysis with Air Resistance Correction
A 0.5 kg ball is thrown vertically upward with an initial speed of 20 m/s. Air resistance does negat
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$$ is subjected to a variable torque d
Variable Force Robotic Arm Power Experiment
In this experiment, a robotic arm exerts a time-varying force on an object as it moves along a horiz
Variable Force Work Calculation and Kinetic Energy Analysis
Consider an object moving along the x-axis under the influence of a variable force given by $$F(x) =
Variable Friction and Kinetic Energy Loss
A 5 kg block slides across a horizontal surface and comes to rest. The frictional force acting on th
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 Circular Motion
A 2-kg mass is attached to a string and constrained to move on a frictionless vertical circular path
Work by Non-Conservative Forces in a Loop
A block experiences a variable nonconservative force along a path given by $$ F(x)= 20 * \sin(x) $$
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 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 in a Variable Force Field along a Curved Path
A particle moves in the xy-plane along the curve defined by $$y = x^2$$ from the point (0, 0) to (2,
Astronaut Recoil upon Throwing an Object
An astronaut of mass 90 kg, floating in space, throws a 1.5 kg tool directly away from her ship at 5
Ballistic Pendulum Analysis
A bullet with mass $$0.02$$ kg is fired horizontally into a pendulum bob of mass $$0.98$$ kg suspend
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 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 for Discrete Particles in the Plane
Three particles are located in the plane with the coordinates and masses given in the table below:
Center of Mass in a Coupled Mass-Spring System
Two masses (m1 = 1.5 kg and m2 = 1.5 kg) are connected by a light spring on a frictionless track. In
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 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,
Central Force and Center-of-Mass Motion in a Binary Star System
A binary star system consists of Star A (mass $$2\times10^{30}\,kg$$) and Star B (mass $$3\times10^{
Conservation of Linear Momentum in Colliding Carts
Two carts on a frictionless track collide. Cart A (mass = 2 kg) moves to the right with a speed of 3
Derivation of the Rocket Equation Using Momentum Conservation
A rocket moving in space expels mass continuously. Assume that during an infinitesimal time interval
Elastic Collision of Gliders
Two gliders undergo an elastic collision on a frictionless air track. Glider A (mass = 1.5 kg) is mo
Elastic Collision: Two Gliders on an Air Track
Two gliders on an air track experience a head-on elastic collision. Glider X (mass = 1 kg) initially
Explosive Separation and Momentum Conservation
A 2 kg projectile traveling at 15 m/s explodes into two equal fragments (1 kg each). One fragment mo
Explosive Separation in a Multi‐Stage Rocket
A multi‐stage rocket undergoes an explosive separation. Experimentally, Stage 1 (mass = 2000 kg) is
FRQ 2: Center of Mass of a Composite Lamina
Consider a composite lamina composed of two rectangular regions in the xy-plane. Region A is 0.8 m b
FRQ 6: Elastic Collision Analysis
Two spheres collide elastically along a straight line. Sphere A (mass = 0.5 kg) initially moves at +
FRQ 11: Experimental Evaluation: Measurement of Center of Mass
A media report claims that a new laser-based method can determine the center of mass of irregular ob
FRQ 14: Derivation of the Continuous Center of Mass Formula
Consider a one-dimensional object with a continuous mass distribution described by the density funct
FRQ 18: Critical Evaluation: Inelastic Collision Study
A published study on vehicle collisions claims that experimental momentum measurements in inelastic
Impulse and Kinetic Energy from a Time-Dependent Force on a Car
A 1200 kg car, initially at rest, is subjected to a time-dependent force given by $$F(t)=4000 - 500*
Impulse and Work: Discerning Differences
A particle of mass 3 kg is subjected to a force that varies with position according to $$F(x)=12*x^2
Impulse from a Time-Varying Force with Graph Stimulus
A force sensor records the force applied to a hockey puck as a function of time while a player strik
Impulse from a Variable Force Function
A force acting on an object varies with time according to the function $$F(t) = 4*t^2$$ (in Newtons)
Inclined Plane: Center of Mass and Impulse Analysis
A block of mass $$3$$ kg rests on a frictionless inclined plane with an angle of $$30^\circ$$. The i
Inelastic Collision on a Frictionless Surface
Two gliders on a frictionless air track collide and stick together. Glider A (mass = 2 kg) moves rig
Inelastic Collision with a Movable Platform
A 0.3 kg ball moving horizontally at 8 m/s collides with and sticks to a 1.2 kg movable platform tha
Inelastic Collision: Combined Motion
A 0.6 kg ball moving at 4.0 m/s collides head-on with a 0.4 kg ball that is initially at rest. The b
Inelastic Collision: Two Blocks on a Frictionless Surface
Block A (mass = 5 kg, initial velocity = 2 m/s) and Block B (mass = 3 kg, initially at rest) collide
Momentum Conservation in Glider Collisions on an Air Track
In a laboratory experiment, students investigate conservation of momentum by allowing two gliders to
Motion of the Center of Mass Under an External Force
A system consists of two particles with masses 2 kg and 3 kg located at x = 0 m and x = 4 m, respect
Motion of the Center of Mass Under External Force
Consider a system consisting of two point masses connected by a light rod. Mass m1 = 2 kg is located
Multi-Dimensional Inelastic Collision Analysis
Two particles undergo a perfectly inelastic collision. Particle A (mass = 2 kg) moves with velocity
Non-Uniform Rod Analysis
A 1.0 m long rod has a linear density given by $$\lambda(x) = 10 + 6*x$$ (kg/m) where x is measured
Oblique Collision of Ice-Hockey Pucks
Two ice-hockey pucks collide on frictionless ice. Puck A (mass = 0.2 kg) moves east at 5 m/s, and Pu
Projectile Explosion and Center of Mass Motion
A 5 kg projectile is launched vertically upward. At its highest point, it explodes into two fragment
Ramp Push Experiment: Variable Force Integration
In a laboratory experiment, a cart on a frictionless ramp is pushed by a force that varies with time
Rocket Propulsion with Variable Mass
A rocket has an initial mass of $$M_0 = 50$$ kg (including fuel) and ejects fuel such that its mass
Rolling Cylinder on an Incline
A uniform solid cylinder (mass = 4 kg, radius = 0.5 m) rolls without slipping down a 30° incline. An
Rotational Dynamics of a Composite Object
A composite object consists of two connected rods: Rod A is 1 m long and has uniform density, while
Rotational Impulse in a Spinning Disc Experiment
In an experiment to measure angular impulse, a student applies a variable torque to a spinning disc
Stability of a Suspended Mobile
A suspended mobile consists of three masses hanging from strings attached to a horizontal bar. The m
Structural Stability: Crane Center of Mass Analysis
An engineer is analyzing a crane consisting of a 500-kg horizontal beam whose center of mass is at 5
Two-Ball Collision Dynamics
Two balls collide head-on in a controlled experiment. The red ball (mass = 0.5 kg) moves to the righ
Acceleration of a Rotating Rigid Body with Frictional Torque
A disk with moment of inertia $$I=2\text{ kg\cdot m}^2$$ experiences a frictional torque proportiona
Analysis of Angular Displacement in a Rotating Disk
In this experiment, several dots are marked along the radius of a rotating disk. The students record
Angular Displacement and Kinematics Analysis
A researcher is investigating the kinematics of a rotating disk. The disk rotates about its center,
Angular Impulse and Change in Angular Momentum
Design an experiment to measure the angular impulse delivered to a rotating object and its resulting
Angular Kinematics Analysis Using Graphical Data
A rotating disk's angular velocity is given by the graph below. Determine key kinematic quantities f
Angular Kinematics on a Rotating Platform
A rotating platform starts from rest and accelerates with a constant angular acceleration $$\alpha$$
Combined Translational and Rotational Dynamics
A rolling disk collides elastically with a spring, causing the spring to compress before the disk re
Composite Body Rotation
A composite object is formed by welding a solid disk to a thin rod. The disk has mass $$M$$ and radi
Computational Modeling of a Spinning Disk with Variable Torque
A spinning disk with a constant moment of inertia of $$I = 0.3\,kg\,m^2$$ is subjected to a time-var
Conservation of Angular Momentum in Explosive Separation
A rotating disk of mass $$M = 5.0 \text{ kg}$$ and radius $$R = 0.5 \text{ m}$$, spinning at $$\omeg
Coupled Rotational and Translational Dynamics in a Rolling Sphere
A sphere is allowed to roll down a curved track without slipping. The experiment examines the coupli
Cylinder Rolling on an Incline
A solid cylinder of mass M rolls without slipping down an inclined plane of height h and length L (w
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
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.
Effect of Friction on Rotational Motion
Design an experiment to quantify the torque losses due to friction in a rotating apparatus. Your goa
Effect of Variable Applied Torque on Angular Acceleration
In a controlled experiment, a variable torque is applied to a rotating disk. The resulting change in
Energy Analysis in Rolling Motion
A spherical ball of mass $$M$$ and radius $$R$$ rolls without slipping down an inclined plane of ver
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
Equilibrium Analysis in a Rotating Beam System
In a lab experiment, a student investigates the equilibrium of a beam pivoted at its center with var
Equilibrium Analysis in Rotational Systems
A uniform beam is balanced on a pivot, with forces applied at various distances from the pivot to ma
Experimental Data: Angular Velocity vs Time Analysis
An experiment records the angular velocity of a rotating object over time. The provided graph shows
Experimental Investigation of Rolling Without Slipping
An experimental apparatus is used to study rolling without slipping for various cylindrical objects.
FRQ 8: Variable Torque and Angular Acceleration
A rotating wheel with constant moment of inertia \(I = 2.00\,kg\cdot m^2\) experiences a time-depend
FRQ 19: Oscillatory Rotational Motion (Torsional Pendulum)
A torsional pendulum consists of a disk suspended by a wire. The restoring torque is given by $$\tau
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
Influence of Friction on Rolling Without Slipping
An experiment investigates the effect of surface friction on rolling objects. The angular velocity o
Integration of Rotational Inertia: Thin Shell vs. Solid Sphere
Derive the moments of inertia for two spherical objects about an axis through their centers: (a) A
Investigating Non-uniform Density Effects on Moment of Inertia
Design an experiment to determine the moment of inertia for an object with a non-uniform mass distri
Lever and Torque Computations
This problem involves calculating torque in a lever system. A diagram is provided below.
Mathematical Modeling of Brake Systems
A braking system applies a constant torque of $$\tau = 15 \text{ Nm}$$ on a flywheel with moment of
Parallel Axis Theorem Application in Complex Systems
A composite object consists of a uniform rod of mass $$M = 4\,kg$$ and length $$L = 3\,m$$, and an a
Parallel Axis Theorem: Composite Body Moment of Inertia
Consider a composite object consisting of a solid disk (mass $$M = 4.0 \text{ kg}$$, radius $$R = 0.
Rolling Cylinder Down an Incline
A solid cylinder rolls without slipping down an incline. A set of measurements were made at differen
Rolling Motion Dynamics Down an Incline
A solid cylinder with mass $$M = 3\,kg$$ and radius $$R = 0.2\,m$$ rolls without slipping down an in
Rolling Motion of a Sphere on an Incline
A solid sphere of mass M and radius R rolls without slipping down an inclined plane of height h star
Rolling Motion with Transition from Slipping to Pure Rolling
A solid sphere of mass m and radius R is initially sliding and rolling down an inclined plane with a
Rotational Inertia of a Composite Bead System
A researcher is investigating the effect of discrete mass distribution on the rotational inertia of
Rotational Inertia of a Non-Uniform Disk
A disk of radius R has a surface mass density given by $$\sigma(r)= \sigma_0 \left(1+\frac{r}{R}\rig
Rotational Inertia of a Uniform Rod
A uniform, thin rod of length $$L$$ and mass $$m$$ rotates about an axis perpendicular to the rod th
Rotational Kinetic Energy Storage in a Flywheel
An engineer is tasked with designing a flywheel energy storage system. The flywheel is required to s
Time-varying Angular Acceleration in a Rotational System
A disk experiences an angular acceleration described by $$\alpha(t)=5\sin(2t) \text{ rad/s}^2$$.
Time-Varying Torque and Angular Acceleration
A researcher is exploring the effects of a time-varying torque on the rotational motion of a rigid b
Torque and Rotational Inertia: Uniform Rod
A uniform rod of length $$L = 2.0 \text{ m}$$ is pivoted about one end. A force of $$F = 10 \text{ N
Torque on a Lever Arm
A lever arm is used to apply force at an angle. Consider a force of $$50*N$$ applied at an angle of
Torque, Friction, and Rotational Equilibrium in a Pulley
A pulley with radius 0.3 m and moment of inertia 0.15 kg m^2 is subjected to a tangential force of 2
Calculus Derivative Analysis in SHM
Given an oscillator with a position function $$y = 0.05 \sin(12t + \frac{\pi}{6})$$, where $$y$$ is
Calculus-Based Prediction of Maximum Speed
A photogate system is set up to record the speed of a mass-spring oscillator. Answer the following p
Comparative Analysis of Horizontal and Vertical SHM Systems
A researcher compares the oscillations of a mass attached to a spring in horizontal and vertical con
Comparative Dynamics of Mass-Spring and Pendulum Oscillators
Analyze the motion of two oscillatory systems: a mass-spring oscillator and a simple pendulum (using
Comparison of Horizontal and Vertical Oscillations
Compare a mass-spring oscillator on a frictionless horizontal surface with a vertical spring-block s
Complex SHM: Superposition of Two Harmonic Motions
A block experiences two independent harmonic motions such that its displacement is given by $$x(t)=
Composite Oscillator: Two Springs in Series
A block with mass $$m = 1.0\,kg$$ is attached to two springs connected in series, with spring consta
Deriving the General Solution of SHM
Derive and analyze the general solution for simple harmonic motion from the governing differential e
Determination of Angular Frequency from Displacement Data
Displacement measurements for a spring-mass oscillator are given by the equation $$y = A\sin(\omega
Determination of the Spring Constant from Experimental Force-Displacement Data
In an experiment to determine the spring constant, a series of force and displacement measurements w
Determining Oscillation Frequency from Acceleration Data
An accelerometer attached to a mass-spring system records acceleration data during oscillations. The
Determining Spring Constant from Force-Displacement Data
In a laboratory experiment, the force exerted by a spring is measured for various displacements. The
Energy Conservation in a Mass–Spring Oscillator
Examine energy conservation in a mass–spring system and its experimental verification.
Energy Conservation in a Simple Pendulum
A simple pendulum of length $$L$$ and mass $$m$$ is displaced by a small angle $$\theta$$ from the v
Energy Distribution and Phase Analysis
An experiment on a spring-mass oscillator is conducted to study the distribution of kinetic and pote
Energy Transformations in SHM
Consider a block attached to a spring undergoing simple harmonic motion with displacement $$x(t)=A\s
Experimental Analysis of SHM Data
The displacement data for a mass-spring system were recorded during a laboratory experiment. The fol
FRQ 2: Energy Conversion in a Spring Oscillator
A block attached to a spring oscillates on a frictionless surface. The following table presents expe
FRQ 9: Damped Oscillatory Motion Analysis
An oscillator experiencing damping shows a decrease in amplitude over successive cycles. Analyze the
FRQ 16: Maximum Speed in SHM via Energy Methods
Experimental data for a mass–spring oscillator, including amplitude, mass, spring constant, and meas
FRQ 17: Determination of Damping Coefficient
An oscillatory system exhibits damping, with its amplitude decreasing over successive cycles. Analyz
FRQ3: Kinematics of SHM – Period and Frequency
A block-spring oscillator is observed to take 0.4 s to travel from its maximum displacement in one d
FRQ6: Calculus Derivation of Velocity and Acceleration in SHM
For a mass undergoing simple harmonic motion described by the displacement function $$x(t)= A\sin(\o
FRQ12: Phase Shift and Time Translation in SHM
An oscillator is described by the equation $$x(t) = A\sin(\omega t+\phi_0)$$. Answer the following:
FRQ20: Energy Dissipation in Damped Pendulum Oscillations
A damped pendulum oscillates with small angles such that its motion is approximately described by $
Graphical Analysis of SHM Experimental Data
A block attached to a horizontal spring oscillates, and its displacement $$x(t)$$ (in meters) is rec
Horizontal Mass-Spring Oscillator Analysis
A laboratory experiment involves a block of mass $$m = 0.50\,kg$$ attached to a horizontal spring of
Lagrangian Mechanics of the Simple Harmonic Oscillator
A researcher employs Lagrangian mechanics to analyze a mass-spring oscillator. Consider a mass $$m$$
Mass-Spring Differential Analysis
Consider a block of mass $$m$$ attached to a horizontal spring with spring constant $$k$$. The block
Oscillations of a Liquid Column in a U-tube
A U-tube containing a liquid with density $$\rho$$ exhibits oscillatory motion when the liquid is di
Pendulum Approximation and Small-Angle Motion
A simple pendulum of length $$L$$ oscillates with small amplitude. Using the small-angle approximati
Pendulum Motion: Small Angle Approximation and Beyond
A simple pendulum consists of a mass $$m = 0.3 \; kg$$ attached to a massless rod of length $$L = 1.
Pendulum Oscillation Experiment: Frequency and Energy Analysis
A simple pendulum consists of a bob of mass $$m = 0.2\;kg$$ attached to a massless string of length
Pendulum Period Measurement Experiment
A group of students measure the period of a simple pendulum by timing multiple oscillations using a
Phase Constant and Sinusoidal Motion
A mass-spring system oscillates according to $$x(t) = A \sin(\omega t + \phi_0)$$ with an amplitude
Phase Space Analysis of SHM
A student plots the phase space diagram (velocity vs. displacement) of a simple harmonic oscillator
Sinusoidal Oscillator and Phase Constant
A mass attached to a spring oscillates horizontally on a frictionless surface, and its displacement
Spring-Block Oscillator: Phase Angle and Motion Description
A block attached to a horizontal spring oscillates without friction. The motion of the block is desc
Systematic Error Analysis in SHM Experiments
The table below shows measured time intervals and displacements from several trials in an experiment
Time-Dependent Length in a Variable-Length Pendulum
In an experiment, a pendulum has a length that varies with time according to the relation $$L(t)=L_0
Vertical Mass-Spring Oscillator: Equilibrium and Oscillations
A 2.0-kg mass is attached to the end of a vertical spring with a force constant $$k = 250\,N/m$$. Th
Analysis of a Gravitational Potential Energy Graph
A graph representing gravitational potential energy as a function of distance is provided below. The
Analyzing a Two-Body Gravitational Interaction Using Calculus
Consider two objects of masses $$m_1$$ and $$m_2$$ that are initially at rest and start moving towar
Areal Velocity and Angular Momentum in Planetary Motion
A planet of mass $$m$$ orbits a star while conserving its angular momentum $$L$$. Answer the followi
Average Orbital Energy and Angular Momentum
For an orbiting satellite, the specific orbital energy and angular momentum are key conserved quanti
Cannonball Trajectory in a Non-Uniform Gravitational Field
An experiment studies the trajectory of a cannonball launched at a high angle to analyze projectile
Center of Mass in a Two-Body System
In a two-body system, such as a planet and its moon, both bodies orbit around their common center of
Comparative Analysis of Orbital Periods for Different Planets
Two planets orbit a star. (a) Derive the relationship $$\frac{T^2}{a^3} = \text{constant}$$ for thes
Comparative Analysis of Planetary Orbits
Two planets orbit the same star with different semimajor axes. Use Kepler's Third Law to analyze and
Deriving Gravitational Potential from Gravitational Force
The gravitational potential \(V(r)\) is related to the gravitational force by calculus. (a) Show th
Determining the Center of Mass in a Celestial System
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Analyze the provided energy data for a planet at apoapsis and periapsis in its orbit. Discuss how co
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Orbital Dynamics: Gravitational Force Variation
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Orbital Energy and Conservation Laws
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Orbital Motion of a Satellite
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Orbital Perturbations from Impulsive Thrust
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Satellite Orbital Decay with Atmospheric Drag Consideration
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Simulating Satellite Orbital Decay and Atmospheric Drag
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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.