The cosine form assumes the object starts at $x = +A$ when $t = 0 (released$ from maximum

Oscillations - OCR A-Level Physics

x = A\cos(\omega t)

v = -A\omega\sin(\omega t)

The cosine form assumes the object starts at $x = +A$ when $t = 0$ (released from maximum positive displacementThe distance moved in a particular direction from a starting point. A vector quantity. Measured in metres (m).).
VelocityThe rate of change of displacement. A vector quantity. Measured in m s⁻¹. is the derivative of displacementThe distance moved in a particular direction from a starting point. A vector quantity. Measured in metres (m).: $v = dx/dt$.
The maximum velocityThe rate of change of displacement. A vector quantity. Measured in m s⁻¹. occurs at $x = 0$ (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..) and has magnitude $v_{max} = A\omega$.
The maximum accelerationThe rate of change of velocity. A vector quantity. Measured in m s⁻². occurs at $x = \pm A$ and has magnitude $a_{max} = A\omega^2$.
Velocity leads displacementThe distance moved in a particular direction from a starting point. A vector quantity. Measured in metres (m). by $\pi/2$ radians ($90^\circ$). AccelerationThe rate of change of velocity. A vector quantity. Measured in m s⁻². leads velocity by $\pi/2$ radians.

Common Mistake MEDIUM

Wrong: Using degrees instead of radians in $\omega t$ when using sin/cos on a calculator.
Right: Always set your calculator to RADIANS mode when working with SHM equations. $\omega t$ is in radians.