Simple harmonic motion test with answers for A Level physics (free PDF download)

Quick answer: Simple harmonic motion is repeated oscillation where the acceleration is proportional to the displacement from equilibrium and points towards it, a = −ω²x. This Physics 11-12 test on simple harmonic motion has 8 questions worth 20 marks, to do in 45 minutes: identify SHM, pendulum on a hook and spring oscillator. The mark scheme is on a separate page; free printable PDF.

This test lasts 45 minutes and is worth 20 marks. Use g = 9.81 m/s² where needed, show every step of your working and give answers with units and sensible significant figures.

Level: Physics grades 11-12 (A Level · IB · Class 11-12) · Curriculum: IB C.1

Time: 45 minutes · 8 questions · Total: 20 marks · Calculator allowed

Contents

Question 1 Identify SHM (2 marks)

Four accelerations are given in SI units: (i) a = −9x, (ii) a = −9x², (iii) a = +9x, (iv) a = −9.

State which one is SHM and give a reason. (1 mark)
Calculate its period. (1 mark)

Question 2 Pendulum on a hook (3 marks)

A pendulum has a length of 1.50 m (pivot to centre of bob). Take g = 9.81 m/s².

Calculate its period for small swings. (2 marks)
State the effect on the period of using a bob of twice the mass. (1 mark)

Question 3 Spring oscillator (3 marks)

A 0.15 kg mass oscillates on a horizontal spring of stiffness 30 N/m with amplitude 0.040 m.

Calculate the angular frequency. (1 mark)
Calculate the maximum speed. (1 mark)
Calculate the maximum acceleration. (1 mark)

Question 4 Energy graph sketch (3 marks)

Sketch on one set of axes the variation of kinetic energy, potential energy and total energy with displacement from −A to +A. (3 marks)

Question 5 Buoy in the swell (3 marks)

The graph shows a buoy in the sea off Mombasa.

Displacement of a buoy against time.

Read the amplitude and period. (1 mark)
Calculate the angular frequency. (1 mark)
Calculate the maximum speed. (1 mark)

Question 6 Pushing a swing (2 marks)

Explain why a small push applied once every swing can build up a large amplitude, and say what the term for this effect is.

Question 7 Car suspension (2 marks)

Explain why a car suspension is designed to be close to critically damped.

Question 8 Time to move out (2 marks)

A particle in SHM has period 0.50 s and amplitude 0.080 m. It starts at the centre. Calculate the time taken to reach x = 0.040 m for the first time.

Defining equation of SHM? — a = −ω²x

Angular frequency in terms of period? — ω = 2π/T

Maximum speed in SHM? — v = ωA at the centre

Maximum acceleration in SHM? — a = ω²A at the ends

Period of a mass on a spring? — T = 2π√(m/k)

Period of a simple pendulum? — T = 2π√(L/g), small angles

Total energy of SHM? — E = ½kA² = ½mω²A²

Speed at displacement x? — v = ω√(A² − x²)

What is resonance? — Large amplitude when driving frequency equals natural frequency

What is critical damping? — Fastest return to equilibrium with no overshoot