Physics · OCR H556 · Topic 5.3

Oscillations

Simple harmonic oscillations, energy of a simple harmonic oscillator, damping.

  • 3 sub-topics
  • Taught in Year 13
  • 35 practice questions
  • 3 animated lessons
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What the specification says

Every sub-topic OCR can examine in this topic, with its reference number from the official specification. The Y12 and Y13 tags show when each sub-topic is usually taught.

  1. 5.3.1Simple harmonic oscillationsY13
  2. 5.3.2Energy of a simple harmonic oscillatorY13
  3. 5.3.3DampingY13

Try 3 questions

Easy, medium and hard questions from this topic, each with a worked solutions and the mark for every step. All 35 questions in this topic, free, no account needed.

Oscillations

Not needed for Year 12Easy

Resonance · Year 13 · 1 mark

  1. A system is forced to oscillate by a periodic driving force. When does resonance occur?
    (1)

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  1. At resonance, energy is transferred to the system most efficiently and the amplitude is a maximum.C: When the driving frequency equals the natural frequency of the system

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Oscillations

Not needed for Year 12Medium

Resonance · Year 13 · 4 marks

A loudspeaker drives a mass on a spring at a slowly increasing frequency.
  1. (a)
    Describe and explain what happens to the amplitude of the mass.
    (3)
  2. (b)
    State the effect of increasing the damping.
    (1)
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Part (a)3 marks

  1. It increases to a maximum, then decreases;
  2. the maximum is when the driving frequency equals the natural frequency (resonance);
  3. then energy is transferred most efficiently.

Part (b)1 mark

  1. The peak amplitude is lower and the peak broader (and shifts to slightly lower frequency).

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Oscillations

Not needed for Year 12Hard

Simple harmonic motion · Year 13 · 12 marks

Figure 1 shows how the displacement x of a 500 g mass on a spring varies with time t. The mass moves with simple harmonic motion.
t / sx / cm0.61.21.82.45−5
Figure 1
  1. (a)
    Use the graph to state the amplitude and the period of the motion.
    (2)
  2. (b)
    Calculate the angular frequency of the motion.
    (2)
  3. (c)
    Calculate the maximum speed of the mass.
    (2)
  4. (d)
    Calculate the maximum acceleration of the mass.
    (2)
  5. (e)
    Calculate the total energy of the oscillation.
    (2)
  6. (f)
    State a time, during the first oscillation, at which the kinetic energy of the mass is a maximum. Explain your answer.
    (2)

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Part (a)2 marks

  1. The greatest displacement from equilibrium.Amplitude = 5 cm
  2. The time for one complete oscillation.Period = 1.2 s

Part (b)2 marks

  1. Angular frequency from the period.ω\omega=2πT{}= \frac{2\pi}{T}=2π1.2{}= \frac{2\pi}{1.2}
  2. ω\omega=5.24 rad s−1{}= 5.24\ \mathrm{rad\,s^{-1}}

Part (c)2 marks

  1. Use the amplitude in metres.vmaxv_{max}=ωA{}= \omega A=5.24×0.05{}= 5.24 \times 0.05
  2. vmaxv_{max}=0.262 m s−1{}= 0.262\ \mathrm{m\,s^{-1}}

Part (d)2 marks

  1. The acceleration is greatest at maximum displacement.amaxa_{max}=ω2A{}= \omega^2 A=5.242×0.05{}= 5.24^2 \times 0.05
  2. amax=1.37 m s−2a_{max} = 1.37\ \mathrm{m\,s^{-2}}

Part (e)2 marks

  1. The total energy equals the kinetic energy at the equilibrium position.EE=12mvmax2{}= \tfrac{1}{2}m v_{max}^2=12×0.5×0.2622{}= \tfrac{1}{2} \times 0.5 \times 0.262^2
  2. E=0.0171 JE = 0.0171\ \mathrm{J}

Part (f)2 marks

  1. Read where the graph crosses the time axis.t = 0.3 s (or 0.9 s)
  2. The gradient of the graph is steepest there.The displacement is zero, so the mass is at the equilibrium position, where its speed is greatest.

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