Quick answer: Simple harmonic motion (SHM) is repeating motion in which the net force is proportional to the displacement from equilibrium and points back toward it, F = −kx. This AP Physics 1 test on simple harmonic motion has 8 questions worth 20 marks, to do in 45 minutes: define SHM, spring period and pendulum design. The mark scheme is on a separate page; free printable PDF.
This test has 8 questions worth 20 marks. It mixes calculations, graph reading, an experimental design and a paragraph argument, as in AP Physics 1 free-response questions. Use g = 9.81 N/kg and give answers with units.
Level: AP Physics 1 (algebra-based) · Curriculum: AP P1 Unit 7
Question 1 Define SHM (2 marks)
State the two conditions that the net force must satisfy for an object to perform simple harmonic motion.- State the relationship between the force and the displacement. (1 mark)
- State the direction of the force. (1 mark)
Question 2 Spring period (2 marks)
A 0.18 kg mass oscillates on a spring with k = 72 N/m.- Calculate the period. (1 mark)
- Calculate the frequency. (1 mark)
Question 3 Pendulum design (2 marks)
A pendulum has a length of 1.60 m, measured from the pivot to the centre of the bob, and swings through a small angle. Use g = 9.81 N/kg.- Calculate its period. (1 mark)
- Calculate the length needed for a period of 1.00 s. (1 mark)
Question 4 Graph analysis (3 marks)
The graph shows a mass on a spring in Kofi’s lab.- Read the amplitude and the period. (1 mark)
- State one time at which the kinetic energy is greatest and explain your choice. (1 mark)
- Calculate the greatest speed using v = 2πA/T. (1 mark)
Question 5 Changing amplitude (2 marks)
A student doubles the amplitude of a spring oscillator without changing the mass or the spring.- State what happens to the period and to the greatest speed. (1 mark)
- State by what factor the total energy changes and justify it with an equation. (1 mark)
Question 6 Energy at a point (3 marks)
A 0.50 kg block on a smooth table oscillates on a horizontal spring with k = 80 N/m and amplitude 0.10 m.- Calculate the total energy. (1 mark)
- Calculate the kinetic energy when x = 0.060 m. (1 mark)
- Calculate the speed at that position. (1 mark)
Question 7 Experimental design (3 marks)
Design an experiment to test whether the period of a hanging mass-spring system depends on the amplitude.- Name the independent and dependent variables. (1 mark)
- Describe how you would measure the period accurately and name two controlled variables. (1 mark)
- State the result you would expect and how the data would show it. (1 mark)
Question 8 Heavier bob claim (3 marks)
Aarav claims that a heavier pendulum bob swings with a shorter period because gravity pulls harder on it. Write a short paragraph that evaluates this claim, using forces and the equation for the period.
