Struck Pendulum

A pendulum of mass $M$ and length $L$ hangs at rest. At time $t = 0$, the pendulum is struck sharply and given a horizontal speed to the right of $v_0$ such that its initial kinetic energy is much less than $MgL$.

a) What is the natural frequency of the pendulum?

b) What are $s(t)$ and $v(t)$ (position and velocity of the mass $M$ on the arc as functions of time)?

c) Show the derivation of the equations of motion used to get the answers to a) and b). Why was it important that the initial kinetic energy be $<< MgL$?