Simple harmonic motion

Harmonic motion (oscillation) is described by the displacement equation:

$x(t)=A\sin(\omega t+\varphi),\qquad \omega=\frac{2\pi}{T}$

where $A$ is the amplitude, $\omega$ — the angular frequency, $\varphi$ — the initial phase. Differentiating, we obtain the velocity and acceleration:

$v=A\omega\cos(\omega t+\varphi)\qquad a=-A\omega^2\sin(\omega t+\varphi)=-\omega^2 x$

The velocity is greatest at the equilibrium position ($x=0$), and the acceleration — at the extreme displacement. The calculator computes x, v, a at a given instant together with the maximum values $v_{max}=A\omega$, $a_{max}=A\omega^2$.