Question

A mass m is at rest on the end of a spring of spring constant k. At t = 0s, it is given an impulse J by a hammer. Write the formula for the subsequent motion in terms of m, k, J and t.

Answer 1

$$\omega=\sqrt{\frac{k}{m}}\\v=\frac{J}{m}\cos \omega t\\x=\frac{J}{m\omega}\sin \omega t$$