Simple Harmonic Motion

Equilibrium Position

The position where the object would rest if all energy was removed from the system

Oscillations

periodic back and forth motions

Displacement in SHM

How far object is from equilibrium position. One side of the equilibrium position has a positive displacement, and the other side has a negative displacement.

Amplitude

Distance between the crest (or trough) of a wave and its equilibrium position. Maximum distance from the equilibrium position during oscillation. Not dependent on mass, but on the amount of initial displacement.

Time period, T

amount of time taken for an oscillator to complete one full cycle. measured in seconds

Frequency, f

Inversly related to frequency. The number of cycles completed per second. Measured in hertz (Hz) (which is equivalent to s⁻¹).

Simple Harmonic Motion

repeated motion around an equilibrium position where the acceleration of the object is proportional to its displacement, but in the opposite direction. The gradient of the graph is equivalent to the square of the angular frequency and, because acceleration and displacement are in opposite directions, it is negative.

Angular frequency

angle that an oscillator covers per second (rad s⁻¹)

Equation for time period using angular frequency

T=2π/ω

Equation for simple harmonic motion

a=-ω²x

• ω= angular velocity (rad s⁻¹)