Simple Harmonic Motion (CIE A Level Physics)

• Simple harmonic motion (SHM) is a specific type of oscillation
• SHM is defined as:

A type of oscillation in which the acceleration of a body is proportional to its displacement, but acts in the opposite direction

 

• Examples of oscillators that undergo SHM are:
  • The pendulum of a clock
  • A mass on a spring
  • Guitar strings
  • The electrons in alternating current flowing through a wire

  

Examples of Simple Harmonic Motion

A pendulum, bungee jumper, swing bridge, vibrations in a prayer bowl, a swing, a ball rolling up and down the sides of a bowl and a spring are all examples of simple harmonic oscillations.

 

• For an object to oscillate specifically in SHM, it must satisfy the following conditions:
  • Periodic oscillations
  • Acceleration proportional to its displacement
  • Acceleration in the opposite direction to its displacement

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

a ∝ −x

• An object in SHM will also have a restoring force to return it to its equilibrium position
• This restoring force will be directly proportional, but in the opposite direction, to the displacement of the object from the equilibrium position
• Note: the restoring force and acceleration act in the same direction

Restoring Force and Acceleration on a Pendulum

Force, acceleration and displacement of a pendulum in SHM

• This is why a person jumping on a trampoline is not an example of simple harmonic motion:
  • The restoring force on the person is not proportional to their distance from the equilibrium position
  • When the person is not in contact with the trampoline, the restoring force is equal to their weight, which is constant
  • This does not change, even if they jump higher

 Girl Bouncing on a Trampoline

Bouncing on a trampoline is not an example of simple harmonic motion because the restoring force is not proportional to the displacement from the equilibrium position