A simple pendulum consists of a rod AC of length 2L (without mass) and a point mass M at C.
A spring, of stiffness K, attached to the rod at B (where AB=L).
A damper, of damping constant c, attached also to the rod at point C.
1) Find the equation of motion of the system (We consider O is small).
2) Determine the Damping Ratio and the natural Frequency n (as a function of K, c, M and L).
3) Find the free vibrations of the system (solution of the
equation of motion) if at t=0, 0 (o) = 0, and 0 (o) = 0.