OCR A Level Physics

Revision Notes

5.5.3 Conditions for Simple Harmonic Motion

Test Yourself

Simple Harmonic Motion

  • Simple harmonic motion (SHM) is a specific type of oscillation
  • An oscillation is said to be SHM when:

The acceleration of a body is proportional to its displacement but acts in the opposite direction

  • Acceleration a and displacement x can be represented by the defining equation of SHM:

a ∝ −x

  • The two conditions required for an object to be simple harmonic motion are therefore:
    • The acceleration is proportional to the displacement
    • The acceleration is in the opposite direction to the displacement

SHM pendulum, downloadable AS & A Level Physics revision notes

Force, acceleration and displacement of a pendulum in SHM

Worked example

Explain why a person jumping on a trampoline is not an example of simple harmonic motion.

Step 1: Recall the conditions for simple harmonic motion

    • The conditions required for SHM:
      • The restoring force/acceleration is proportional to the displacement
      • The restoring force/acceleration is in the opposite direction to the displacement

Step 2: Consider the forces in the scenario given

    • When the person is not in contact with the trampoline, the restoring force is equal to their weight, which is constant
    • The value of their weight does not change, even if they jump higher (increase displacement)

Step 3: Write a concluding sentence

    • The restoring force on the person is not proportional to their distance from the equilibrium position, therefore, this scenario does not fulfil the conditions for SHM

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