Edexcel IAL Physics: Oscillations — Practice Questions

These are original questions written for Marlbridge, in the style and at the standard of the examination. They are not reproduced past-paper questions — examination boards hold copyright in their own papers. Use these alongside the official past papers available free from your board.

Related: Oscillations revision notes

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Section A

1. Define simple harmonic motion. [2]

2. State the relationship between period and frequency, and between angular frequency and period. [2]

Section B

3. A mass on a spring oscillates with amplitude 0.040 m and frequency 2.5 Hz.

(a) Calculate the angular frequency. [2] (b) Calculate the maximum speed. [2] (c) Calculate the maximum acceleration and state where it occurs. [3]

4. Describe how the kinetic and potential energy of an oscillator vary over one complete cycle, and state what happens to the total energy. [4]

5. A simple pendulum has a length of 0.80 m.

(a) Calculate its period. Take g = 9.81 m s⁻². [3] (b) State the effect on the period of doubling the mass of the bob, and explain. [2]

6. Explain the terms damping and resonance.

(a) Distinguish between light, heavy and critical damping. [3] (b) Explain what happens at resonance and how damping affects the resonance peak. [4] (c) Give one example where resonance is useful and one where it is a hazard. [2]

7. A mass of 0.60 kg oscillates on a spring of spring constant 15 N/m, with amplitude 0.030 m.

(a) Calculate the period of oscillation. [2] (b) Calculate the maximum acceleration, stating where it occurs. [2]

8. An unknown mass is attached to a spring of known spring constant and set oscillating, and its resonant frequency is measured.

(a) Explain how the resonant frequency of a mass-spring system can be used to determine the unknown mass. [2] (b) State one precaution needed to obtain an accurate value of the resonant frequency in this experiment. [1]

9. A real oscillating structure, such as a bridge, loses energy over successive cycles even though it is not deliberately fitted with a damper.

(a) Name two mechanisms by which this structure loses energy. [2] (b) Explain why this energy loss means the total mechanical energy is not conserved by the oscillator alone. [1]

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Answers

1. Motion in which the acceleration is directly proportional to the displacement from a fixed equilibrium point [1] and is always directed towards that point [1].

2. f = 1 ÷ T [1]; ω = 2π ÷ T = 2πf [1].

3. (a) ω = 2πf = 2π × 2.5 [1] = 15.7 rad s⁻¹ [1]. (b) v_max = ωA = 15.7 × 0.040 [1] = 0.63 m s⁻¹ [1]. (c) a_max = ω²A = 15.7² × 0.040 [1] = 9.9 m s⁻² [1]; it occurs at maximum displacement, i.e. at the ends of the oscillation [1].

4. At maximum displacement the kinetic energy is zero and the potential energy is at its maximum [1]. At the equilibrium position the kinetic energy is maximum and the potential energy is zero [1]. Each therefore varies between zero and the same maximum value, twice per cycle [1]. In the absence of damping the total energy remains constant [1].

5. (a) T = 2π√(l ÷ g) [1] = 2π√(0.80 ÷ 9.81) [1] = 1.79 s [1]. (b) No effect [1] — the mass does not appear in the equation, because the restoring force is proportional to the mass, so the acceleration is independent of it [1].

6. (a) Light damping — the amplitude decreases gradually over many oscillations [1]. Heavy damping — the system returns to equilibrium slowly without oscillating [1]. Critical damping — the system returns to equilibrium in the shortest possible time without overshooting [1]. (b) Resonance occurs when the driving frequency equals the natural frequency of the system [1]; energy is transferred most efficiently to the oscillator [1] and the amplitude reaches a maximum [1]. Increasing the damping reduces the peak amplitude and broadens the peak, shifting it slightly to a lower frequency [1]. (c) Useful: tuning a radio circuit to a station’s frequency, or MRI [1]. Hazard: a bridge oscillating in step with marching feet or wind, risking structural failure [1].

7. (a) T = 2π√(m/k) = 2π√(0.60 ÷ 15) [1] = 2π√0.04 = 2π(0.20) = 1.26 s [1]. (b) ω = 2π ÷ T = 2π ÷ 1.26 = 5.0 rad s⁻¹ [1]; a_max = ω²A = 5.0² × 0.030 = 0.75 m s⁻² [1], occurring at maximum displacement (the ends of the oscillation).

8. (a) The system is driven at a range of frequencies until the amplitude peaks at resonance, where the driving frequency equals the natural frequency [1]. Since the natural frequency of a mass-spring system is fixed by ω = √(k/m), and the spring constant k is already known, the resonant frequency found experimentally can be used to calculate the unknown mass [1]. (b) e.g. vary the driving frequency in small steps near the expected resonance so the peak is not missed between measurements [1]. (Also accept: allow the system to reach a steady amplitude at each frequency before recording it.)

9. (a) Energy is lost to friction/air resistance (damping) [1] and to plastic deformation of the ductile materials within the structure as it flexes [1]. (b) Because energy is continuously transferred out of the oscillating system (to heat, via these mechanisms), the oscillator’s own mechanical energy decreases over time — overall energy is still conserved, but not within the oscillator alone [1].

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Where marks are usually lost

• Defining SHM without stating the direction of the acceleration.
• Using degrees instead of radians for ω.
• Saying the pendulum period depends on the mass.
• Describing resonance without mentioning the natural frequency.
• Forgetting that a mass-spring system’s resonant frequency can be used experimentally to find an unknown mass, given a known spring constant.
• Naming only damping as an energy-loss mechanism in a real structure, when plastic deformation of the material itself also dissipates energy.