Conditions for Simple Harmonic Motion (Edexcel International A Level Physics)

Conditions for Simple Harmonic Motion

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

• An oscillation is said to be SHM when:

  • The acceleration is proportional to the displacement

  • The acceleration is in the opposite direction to the displacement

• 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

• Time period, T:

  • The objects swings are periodic, meaning they are repeated in regular intervals according to their frequency or time period

  • If an object swings freely it always takes the same time to complete one swing

Restoring force

• When an object is moving in SHM a force, called the restoring force, F, is always trying to return the object back to its equilibrium position. 

• The force is proportional to the displacement, x, from that equilibrium position

F = -kx

• Where: 

  • F  is the restoring force

  • x is the displacement of the object from the equilibrium position

  • k is a constant depending on the system

  • the negative sign shows that the acceleration will always be towards the centre of oscillation  

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