OCR A Level Physics A: Simple harmonic motion, energy, damping and resonance (H556) – Practice Questions

These are original questions written for Marlbridge, for revision and practice on this content. They are not reproduced past-paper questions, and they do not replicate the exam’s exact structure, question count or mark tariffs – examination boards hold copyright in their own papers. Use these alongside the official past papers from your board or school.

These questions cover section 5.3 (Oscillations) of the OCR Advanced GCE in Physics A specification (H556), Version 3.0 (March 2026), for first assessment in 2017. Revise with the study guide or the revision notes. Angles are in radians. Take-home check: free diagnostics.

Questions

1. (a) Define simple harmonic motion. [2] (b) State what the minus sign means in a = −ω²x. [1]

2. A piston completes 90 oscillations in 45.0 s. Calculate its period, frequency and angular frequency. [3]

3. Two identical pendulums have period 2.0 s. One passes through equilibrium 0.50 s after the other, moving the same way. Calculate the phase difference in radians. [2]

4. An oscillator has amplitude 0.12 m and angular frequency 5.0 rad s⁻¹. Calculate (a) its maximum speed [1], (b) its maximum acceleration [1], (c) its speed when the displacement is 0.090 m [2], and (d) its acceleration at that displacement [1].

5. A mass oscillates with displacement x = 0.035 sin(18t) in SI units. (a) State the amplitude and calculate the period. [2] (b) Calculate x when t = 0.25 s. [1] (c) Calculate the first time at which x = +0.0175 m. [2]

6. The acceleration-displacement graph of an oscillator is a line through the origin that passes through x = 0.050 m, a = −12.8 m s⁻². (a) Show that the motion is SHM and find ω. [2] (b) Calculate the period. [1] (c) The amplitude is 0.050 m. Calculate the maximum speed. [1] (d) State the phase relation between v and x. [1]

7. A student times a trolley on springs. Twenty oscillations take 31.8 s, with an uncertainty of ±0.2 s for the timing. (a) Describe how to time the oscillations as accurately as you can. [3] (b) Calculate the period and its absolute uncertainty. [2]

8. A 0.25 kg mass hangs from a spring of constant 49 N m⁻¹. (a) Show that the resultant force gives a = −(k/m)x and calculate ω and T. [3] (b) The amplitude is increased from 2.0 cm to 6.0 cm. State what happens to T, the maximum speed and the total energy, with figures. [3]

9. A 0.40 kg oscillator has ω = 7.0 rad s⁻¹ and amplitude 0.10 m. (a) Calculate the total energy. [2] (b) Calculate the kinetic and potential energy at x = 0.060 m. [3] (c) Describe the energy-displacement graphs. [2]

10. A light-damped pendulum has amplitude 9.0 cm, falling to 4.5 cm after some cycles. (a) Calculate the percentage of its energy lost. [2] (b) State where the energy goes. [1] (c) Compare light, critical and heavy damping. [3] (d) Give one use of critical damping. [1]

11. A 0.20 kg mass on a spring of constant 18 N m⁻¹ is driven by a vibrator whose frequency is slowly increased from 0.5 Hz to 3.0 Hz. (a) Calculate the natural frequency. [3] (b) Describe and explain how the amplitude changes. [4] (c) State how the amplitude-driving frequency graph changes if a card is attached to the mass. [2] (d) Give an example of unwanted resonance and one way to reduce it. [2]

Answers

1. (a) The acceleration is proportional to the distance from equilibrium [1] and points back towards equilibrium [1]. [2] (b) The acceleration is opposite in direction to the displacement [1]. [1] Examiner insight: A definition needs proportionality and direction; “back and forth” is too vague to define SHM.

2. T = 45.0/90 = 0.500 s [1]; f = 1/0.500 = 2.00 Hz [1]; ω = 2π × 2.00 = 12.6 rad s⁻¹ [1]. [3] Examiner insight: Keep to the units asked for; rad s⁻¹ and Hz are different.

3. Phase difference = 2π × 0.50/2.0 [1] = π/2 rad (1.57 rad) [1]. [2] Examiner insight: Write the fraction of a period used, which makes your method clear to the reader.

4. (a) vmax = ωA = 5.0 × 0.12 = 0.60 m s⁻¹ [1] [1] (b) amax = ω²A = 25 × 0.12 = 3.0 m s⁻² [1] [1] (c) v = 5.0 × √(0.12² − 0.090²) [1] = 5.0 × 0.0794 = 0.40 m s⁻¹ [1] [2] (d) a = ω²x = 25 × 0.090 = 2.25 = 2.3 m s⁻² (2 s.f.) towards equilibrium [1] [1] Examiner insight: A direction for a in (d) is part of the answer; a bare magnitude leaves the answer incomplete.

5. (a) Amplitude 0.035 m [1]; T = 2π/18 = 0.35 s [1] [2] (b) x = 0.035 sin(4.5) = −0.034 m [1] [1] (c) sin 18t = 0.5, so 18t = π/6 [1], t = 0.029 s [1] [2] Examiner insight: Use radians for the angle; the same expression in degrees gives a different number, so work in radians throughout.

6. (a) a is proportional to −x, with gradient −12.8/0.050 = −256 s⁻² [1], so a = −ω²x with ω² = 256 and ω = 16 rad s⁻¹ [1] [2] (b) T = 2π/16 = 0.39 s [1] [1] (c) vmax = 16 × 0.050 = 0.80 m s⁻¹ [1] [1] (d) v leads x by π/2 [1] [1] Examiner insight: Say “line through the origin with negative gradient” to show it is SHM, not just state it.

7. (a) Use a fiducial marker at the equilibrium position and start and stop the timer as the trolley passes it [1]. Time many (20) oscillations and divide [1]. Repeat and take a mean, with a small steady amplitude [1]. [3] (b) T = 31.8/20 = 1.59 s [1]; uncertainty = 0.2/20 = ±0.01 s [1] [2] Examiner insight: Divide the absolute uncertainty by 20 as well as the time.

8. (a) The resultant force is F = −kx [1], so a = F/m = −(k/m)x with ω² = 49/0.25 = 196 s⁻², ω = 14 rad s⁻¹ [1] and T = 2π/14 = 0.45 s [1]. [3] (b) T stays 0.45 s because the oscillator is isochronous [1]; vmax = 14 × 0.060 = 0.84 m s⁻¹ (three times larger) [1]; energy ½kA² rises from 0.0098 J to 0.088 J (nine times) [1]. [3] Examiner insight: “Nine times” must come from energy being proportional to A², not A.

9. (a) E = ½mω²A² = ½ × 0.40 × 49 × 0.010 [1] = 0.098 J [1] [2] (b) Ek = ½ × 0.40 × 49 × (0.010 − 0.0036) [1] = 0.063 J [1]; Ep = 0.098 − 0.063 = 0.035 J [1] [3] (c) Ep against x is a parabola with minimum at x = 0 and Ek against x is an inverted parabola with maximum at x = 0 [1]; they sum to a horizontal total-energy line at 0.098 J, crossing at x = ±0.071 m [1]. [2] Examiner insight: Check that Ek and Ep add to E; it is a quick test of the arithmetic.

10. (a) Energy is proportional to A², so energy left is (4.5/9.0)² = 0.25 [1]; energy lost is 75% [1]. [2] (b) It is transferred as thermal energy to the surroundings (through friction or drag) [1]. [1] (c) Light damping: oscillations continue with decaying amplitude [1]. Critical damping: settles at equilibrium in the least time with no oscillation [1]. Heavy damping: no oscillation and a slow return [1]. [3] (d) For example a car suspension, a door closer or a meter needle [1]. [1] Examiner insight: Compare all three types in terms of oscillation and return time, not just by name.

11. (a) ω = √(k/m) = √(18/0.20) = 9.49 rad s⁻¹ [1]; f = ω/2π [1] = 1.5 Hz [1]. [3] (b) The amplitude is small at 0.5 Hz [1], rises as the driving frequency approaches 1.5 Hz [1], reaches a maximum at resonance, where the driving frequency has become equal to the natural frequency, because energy transfer is greatest [1], then falls again towards 3.0 Hz [1]. [4] (c) The peak is lower [1] and broader (the maximum moves to slightly lower frequency) [1]. [2] (d) For example a washing machine drum shaking at one spin speed [1]; add damping or change the natural frequency [1]. [2] Examiner insight: Name driving and natural frequency in the same sentence; “frequencies match” is too loose.

Where marks are usually lost

• Leaving out the direction (towards equilibrium) in a = −ω²x.
• Using degrees for the angle in x = A sin ωt.
• Taking amplitude as peak-to-peak distance.
• Forgetting 2π when changing between f and ω.
• Saying energy rises with A, not A².
• Describing a damped oscillation without the loss of energy as thermal energy.
• Leaving the peak position unchanged but taller when damping is added.
• Writing “frequencies match” at resonance without naming driving and natural.

Next steps

• Read the revision notes and the study guide.
• Return to the OCR A Level Physics hub and tick off the checklist.
• Take the free 10-minute diagnostics.
• Book a free trial class.

Official syllabus

OCR Advanced GCE in Physics A (H556) specification, Version 3.0 (March 2026), for first assessment in 2017, published by OCR. Section 5.3, Oscillations.