The defining equation links acceleration, angular frequency, and displacement

Simple Harmonic Motion — AQA A-Level Physics

a = -\omega^2 x

$a$: 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. (m $s^{-2}$)
$\omega$: angular frequencyThe number of complete oscillations passing a point per unit time. Measured in hertz (Hz). (rad $s^{-1}$)
$x$: displacementThe distance moved in a particular direction from a starting point. A vector quantity. Measured in metres (m). from 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.. (m)

The minus sign shows 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. and displacementThe distance moved in a particular direction from a starting point. A vector quantity. Measured in metres (m). are always in opposite directions.
Maximum accelerationThe rate of change of velocity. A vector quantity. Measured in m s⁻². occurs at maximum displacementThe distance moved in a particular direction from a starting point. A vector quantity. Measured in metres (m). ($x = A)$.
Acceleration is zero at 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 ($x = 0)$.
A graph of a against x is a straight line through the origin with gradient -omega^2.

Examiner Tips and Tricks

The a-x graph is the defining test for SHM.
If you get a straight line through the origin with a negative gradient, the motion is SHM.
The gradient gives you omega^2.