- Displacement: distance from the equilibrium position
- Amplitude: the maximum displacement from the equilibrium position
- Period: the time taken to complete one full oscillation
- Frequency: the number of complete oscillations per unit time
Angular frequency describes how quickly an object oscillates.
The defining equation of simple harmonic motion is:
The acceleration is proportional to the displacement and is in the opposite direction. There are two commonly used solutions to this equation:
The velocity of an oscillator undergoing SHM is given by:
From this equation it follows that velocity can vary between 0 (at ) to its maximum values, (at the equilibrium position). It follows that:
The period T of a simple harmonic oscillator is independent of the amplitude A of the oscillator. Such an oscillator is described as isochronous. The shape of a graph of displacement against time is sinusoidal. If no energy is transferred to the surroundings, the amplitude remains constant. The gradient of the displacement-time graph is equal to the velocity, and the gradient of the velocity-time graph is equal to the acceleration.