Suppose that a block of mass $500$g is suspended vertically from a spiral spring whose spring constant is $5$N$/$m$.$ If the spring is pulled downward from its equilibrium position by force P$=5$N$,$ prove, through calculations that once the external force is withdrawn, the block will experience a simple harmonic motion.

Hence, or otherwise, determine:

its periodic time of oscillation and its angular frequency when the external force is withdrawn.