Consider a double pendulum made of two masses, m1 and m2, and two rods of lengths ?1

Question:

Consider a double pendulum made of two masses, m1 and m2, and two rods of lengths ?1 and ?2 (see Fig.). Find the equations of motion. For small oscillations, find the normal modes and their frequencies for the special case ?1 = ?2 (and consider the cases m1 = m2, m1 >> m2, and m1 > ?2, and ?1