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 ($90\degree$). 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.