Derivation of simple pendulum formula

[physicsgal10]

You pull a simple Pendulum of length 0.240 m to the side through an angle of 3.5 degrees and release it.
(a) How much time does it take the pendulum bob to reach its highest speed?
(b) How much time does it take if the pendulum is released at an angle 1.75 degrees instead of 3.5 degrees?

 

[LawrenceC]

Draw a free body diagram so you can write the differential equation for the motion of the pendulum bob. Assume small angle of swing so you can get a differential equation that you can easily solve.