Simple Harmonic Motion (CIE A Level Physics)

• Simple harmonic motion (SHM) is a specific type of oscillation that occurs when acceleration is proportional to displacement from a fixed point and in the opposite direction

 

• An object is said to perform simple harmonic oscillations when all of the following apply:
  
  • The oscillations are periodic (repeating)
  • There is a central equilibrium point known as the fixed point
  • The object's displacement, velocity and acceleration change continuously
  • There is a restoring force always directed towards the fixed point
  • The magnitude of the restoring force is proportional to the displacement
  • The restoring force causes the acceleration

• The restoring force and the acceleration must always be:
  • Directed towards the equilibrium position, and hence, in the opposite direction to the displacement
  • Directly proportional to the displacement

a ∝ −x 

• Where:
  • a = acceleration (m s⁻²)
  • x = displacement (m)

Restoring force, acceleration and displacement

Force, acceleration and displacement of a simple pendulum in SHM

Examples of simple harmonic motion

• Examples of oscillators that undergo SHM are:
  • The pendulum of a clock
  • A child on a swing
  • The vibrations of a bowl
  • A bungee jumper reaching the bottom of his fall
  • A mass on a spring
  • Guitar strings vibrating
  • A ruler vibrating off the end of a table
  • The electrons in alternating current flowing through a wire
  • The movement of a swing bridge when someone crosses
  • A marble dropped into a bowl

  

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.

 

An example of not SHM

• A person jumping on a trampoline is not an example of simple harmonic motion because:
  • The restoring force on the person is not proportional to their displacement from the equilibrium position and always acts down
  • 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

The restoring force of the person bouncing is equal to their weight and always acts downwards