Formula Undamped Harmonic Oscillator Position Amplitude Time Angular frequency Phase
$$y(t) ~=~ A \cos(\omega \, t + \varphi)$$ $$y(t) ~=~ A \cos(\omega \, t + \varphi)$$
Position
$$ y(t) $$ Unit $$ \mathrm{m} $$ Position of the harmonic oscillator at the time \(t\). It can be, for example, the position of the oscillating mass hanging on a spring.
Amplitude
$$ A $$ Unit $$ \mathrm{m} $$ Maximum displacement 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 deflection is \(y(t)\).
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 which deflection \(y(0)\) the harmonic oscillator had at the time \(t=0\):$$ y(0) ~=~ A\,\cos(\varphi) $$