Simple harmonic motion (SHM)
Oscillations - OCR A-Level Physics
Key Definition
Simple harmonic motion (SHM)
Oscillatory motion in which the acceleration is directly proportional to the displacement from the equilibrium position and is always directed towards that equilibrium position.
Oscillatory motion in which the acceleration is directly proportional to the displacement from the equilibrium position and is always directed towards that equilibrium position.
$$a = -\omega^2 x$$
- The negative sign indicates that 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 always in the opposite direction to displacementThe distance moved in a particular direction from a starting point. A vector quantity. Measured in metres (m). (always directed towards 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..).
- $\omega$^2 is a positive constant, so the magnitude of 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 |x|.
- At the equilibrium positionThe central rest position about which an oscillating object moves; the displacement is zero here. (x = 0): $accelerationThe rate of change of velocity. A vector quantity. Measured in m s⁻². = 0$ and velocity is maximum.
- At the amplitudeThe maximum displacementThe distance moved in a particular direction from a starting point. A vector quantity. Measured in metres (m). of a point on a wave from its equilibriumAn object is in equilibrium when the resultant force on it is zero. The object is either stationary or moving at constant velocity. (rest) position. Measured in metres (m). (x = $\pm$A): acceleration is maximum and velocity = 0.
- The motion is isochronousHaving a constant time period regardless of amplitude — a key property of simple harmonic motion for small angles. meaning the periodThe time taken for one complete oscillation or wave cycle. Measured in seconds (s). is independent of the amplitudeThe maximum displacement of a point on a wave from its equilibrium (rest) position. Measured in metres (m). (for true SHM).
Common Mistake
MEDIUM
Wrong: Defining SHM as 'acceleration is proportional to displacementThe distance moved in a particular direction from a starting point. A vector quantity. Measured in metres (m).' without mentioning the direction.
Right: You MUST state that acceleration is proportional to displacement AND 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 velocity. position (or equivalently, in the opposite direction to displacement). Missing the direction condition loses marks.
Right: You MUST state that acceleration is proportional to displacement AND 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 velocity. position (or equivalently, in the opposite direction to displacement). Missing the direction condition loses marks.
Examiner Tips and Tricks
- The mathematical definition a = -$\omega$^2 x contains both requirements: proportionality ($\omega$^2 is constant) and direction (negative sign).
- Stating this equation with definitions of symbols earns full marks for 'define SHM'.