Physics

Simple harmonic motion is governed by a sinusoidal position function, and the key is finding the correct phase constant that matches your initial conditions. Once you know the full equation $x(t) = A\sin(\omega t + \phi)$, taking its derivative gives you velocity at any time. Use the displacement and direction information at $t=0$ to pin down $\phi$, then evaluate the velocity formula at the given time.

Simple harmonic motion is governed by a sinusoidal position function, and the key is finding the correct phase constant that matches your initial conditions. Once you know the full equation $x(t) = A\sin(\omega t + \phi)$, taking its derivative gives you velocity at any time. Use the displacement and direction information at $t=0$ to pin down $\phi$, then evaluate the velocity formula at the given time.