Quick answer: Simple harmonic motion obeys d²x/dt² = −ω²x, with solution x = A cos(ωt + φ). This AP Physics C test on simple harmonic motion has 8 questions worth 20 marks, to do in 45 minutes: spring oscillator, calculus on x(t) and amplitude and period. The mark scheme is on a separate page; free printable PDF.
This test covers simple harmonic motion and physical pendulums in the style of AP Physics C: Mechanics. Show every step, give units and state assumptions such as small angles. You may use a calculator and g = 9.81 m/s². The total is 20 marks.
Level: AP Physics C (Mechanics and E&M, calculus-based) · Curriculum: AP PC:M Unit 7
Question 1 Spring oscillator (2 marks)
A 0.25 kg mass is attached to a spring with k = 100 N/m. Calculate ω and the period.Question 2 Calculus on x(t) (3 marks)
A particle moves with x = 0.060 cos(10t) (SI units).- Calculate the maximum speed. (1 mark)
- Calculate the maximum acceleration. (1 mark)
- Calculate x at t = 0.10 s. (1 mark)
Question 3 Amplitude and period (2 marks)
Explain why the period of a mass on a spring does not depend on the amplitude of the oscillation.Question 4 Energy and speed (3 marks)
A 0.40 kg block on a spring (k = 250 N/m) oscillates with amplitude 0.080 m.- Calculate the total energy. (1 mark)
- Calculate the potential energy at x = 0.040 m. (1 mark)
- Calculate the speed at x = 0.040 m. (1 mark)
Question 5 Physical pendulum (3 marks)
Question 6 Swinging rod (3 marks)
A uniform rod of length 0.60 m is pivoted at one end and swings in a vertical plane through small angles. Calculate its period.Question 7 Doubling the period (2 marks)
A simple pendulum 1.0 m long has a period of 2.0 s. Calculate the length needed to double the period.Question 8 Verify a solution (2 marks)
Show that x = A sin(ωt) satisfies d²x/dt² = −ω²x.
