A physical pendulum is formed by a rod of mass m and length 2L, at the ends there are two masses 2m and m′ are arranged, as shown in the attached figure. The axis of oscillation is horizontal and crosses the rod perpendicularly at its geometric center (E).

a) Determine the energy of the oscillating pendulum and, from this, find the equation of motion of the SHM.

b) While the pendulum is oscillating, the mass m′ is released from the rod. It is observed that the resulting pendulum registers an oscillatory motion whose frequency is just twice the original frequency. Calculate the value of the mass m′.
c) The mass m′ after falling is replaced by another mass 2m which is fixed at a distance x < L from the axis. Verify if there exists a position x that allows to have oscillations of minimum period m 

2m E m m'