3.6.1.2
SHM requires acceleration proportional to and opposite to displacement
Simple Harmonic Motion — AQA A-Level Physics
Key Definition
Simple harmonic motion — An oscillation in which the acceleration is directly proportional to the displacement from the equilibrium position and is always directed towards it.
$$a = -\omega^2 x$$
- Where:
- $a$ = acceleration (m \(s^{-2}\))
- $\omega$ = angular frequency (rad \(s^{-1}\))
- $x$ = displacement (m)
- Two conditions must both be met: (1) accelerationThe rate of change of velocityThe rate of change of displacement. A vector quantity. Measured in m s⁻¹.. A vector quantity. Measured in m s⁻². is proportional to displacementThe distance moved in a particular direction from a starting point. A vector quantity. Measured in metres (m)., (2) accelerationThe rate of change of velocityThe rate of change of displacement. A vector quantity. Measured in m s⁻¹.. A vector quantity. Measured in m s⁻². is in the opposite direction to displacementThe distance moved in a particular direction from a starting point. A vector quantity. Measured in metres (m)..
- Written mathematically: a is proportional to -x.
- The restoring force is always directed towards the equilibriumAn object is in equilibrium when the resultant force on it is zero. The object is either stationary or moving at constant velocityThe rate of change of displacement. A vector quantity. Measured in m s⁻¹.. position.
- The time periodThe time taken for one complete oscillation or wave cycle. Measured in seconds (s). is independent of amplitudeThe maximum displacement of a point on a wave from its equilibrium (rest) position. Measured in metres (m). (for small oscillations).
- Examples of SHM: pendulum, mass on a spring, liquid in a U-tube, vibrating ruler on a table edge.
- Not SHM: a person on a trampoline. The restoring force (weight) is constant and does not vary with displacementThe distance moved in a particular direction from a starting point. A vector quantity. Measured in metres (m)..