Recognize the SHM force condition
Check that the net force points toward equilibrium and is proportional to displacement from it. Distinguish linear SHM from a merely restoring nonlinear force.
AP Physics 1 · Unit 7 · Oscillations
Simple Harmonic Motion Practice Problems
Connect restoring force to the timing, equations, and graphs of a repeating oscillation.
12 questions6 conceptual · 6 calculation
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What you’ll practice
Read the whole oscillation
Find period, frequency, and spring stiffness
Convert between cycles and radians, use mass and stiffness to predict period, and calibrate a spring from a hanging mass before calculating motion with a replacement mass.
Connect equations with motion graphs
Choose a sine or cosine starting state, calculate force at a stated time, and identify velocity and acceleration extrema from a sensor trace. Compare a phase change with a change in mass.
A question from this set
What makes motion simple harmonic?
Which two properties must the net restoring force have for one-dimensional simple harmonic motion about equilibrium?
Try it in the practice setKey ideas
Height, slope, and phase describe different things
A position maximum is a velocity zero
Velocity is the slope of a position–time curve. The steepest falling crossing gives maximum negative velocity; the steepest rising crossing gives maximum positive velocity. Acceleration is opposite to displacement for the ideal linear spring.
A new starting point does not require a new period
Sine and cosine traces can represent the same mass and spring with different clock origins or initial states. Increasing mass by a factor of four doubles the period, while changing amplitude alone leaves the ideal linear-spring period unchanged.
See the physics
Compare sensor traces with native spring motion
After an attempt, run the actual spring–mass model and inspect recorded displacement, velocity, and acceleration versus time. Measure a full period between repeated same-direction crossings, compare mass and amplitude changes, and test a vertical spring about loaded equilibrium. Given sensor graphs remain available before the run.
Use a hint for a starting point or open a worked solution to follow the reasoning. Your progress saves in this browser, so you can return to unfinished questions.
Ready for simple harmonic motion?
Begin with a conceptual question, then work through the calculations.