Formula Undamped Harmonic Oscillator Velocity Amplitude Time Angular frequency Phase
$$v(t) ~=~ -\omega \, A \sin(\omega \, t + \varphi)$$ $$v(t) ~=~ -\omega \, A \sin(\omega \, t + \varphi)$$
Velocity
$$ v $$ Unit $$ \frac{\mathrm m}{\mathrm s} $$ Velocity of the harmonic oscillator at the time \(t\). It can be, for example, the velocity of the oscillating mass hanging on a spring.
Amplitude
$$ A $$ Unit $$ \mathrm{m} $$ Maximum deflection of a harmonic oscillator. In the case of a spring pendulum, it is the maximum distance of the mass from the rest position of the spring (undeflected mass).
Time
$$ t $$ Unit $$ \mathrm{s} $$ Time at which the velocity is \(v(t)\).
Angular frequency
$$ \omega $$ Unit $$ \frac{\mathrm{rad}}{\mathrm s} $$ Angular frequency \(\omega = 2\pi\,f\) describes how fast the harmonic oscillator oscillates.
Phase
$$ \varphi $$ Unit $$ \mathrm{rad} $$ Phase is an angular quantity that determines what velocity \(v(0)\) the harmonic oscillator had at time \(t=0\):$$ v(0) ~=~ -\omega\,A\,\sin(\varphi) $$