A LevelPhysicsAQARevision Notes6. Further Mechanics & Thermal Physics6.2 Simple Harmonic Motion6.2.6 Harmonic Oscillators in Context

Harmonic Oscillators in Context (AQA A Level Physics)

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Harmonic Oscillators in Context

  • Any oscillations about an equilibrium where its restoring force is proportional to its displacement will be simple harmonic
    • For example, liquid in a U-tube

U-tube SHM, downloadable AS & A Level Physics revision notes

Liquid in a U-tube is a type of simple harmonic oscillator with a displacement x from the equilibrium position and length L

T space equals space 2 pi square root of l over g end root

Worked example

Water of length 20 cm is added to a U-tube. When added the water oscillates in simple harmonic motion in a time period T. 

q3a_oscillations_ib-sl-physics-sq-medium

Calculate the frequency of the oscillations.

Step 1: List the known quantities

    • L = 20 cm = 0.20 m

Step 2: From the data booklet

T = 1 over f

f space equals space 2 pi square root of L over g end root

Step 3: Rearrange time period equation for the frequency

f = 1 over T

f = fraction numerator 1 over denominator 2 pi end fractionsquare root of g over L end root

Step 4: Substitute values into the frequency equation, to calculate f:

f equals space fraction numerator 1 over denominator 2 pi end fraction square root of fraction numerator 9.81 over denominator 0.20 end fraction end root

f = 1.11 Hz

Examiner Tip

Don't let these slightly unusual situations confuse you. Try to model each part with each part against a conventional spring or pendulum system. 

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