# 5.5.3 Conditions for Simple Harmonic Motion

## 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

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

### Get unlimited access

to absolutely everything:

• Unlimited Revision Notes
• Topic Questions
• Past Papers