(Solved): A double pendulum consists of two simple pendula, with one pendulum suspended from the bob of the ...

A double pendulum consists of two simple pendula, with one pendulum suspended from the bob of the other. The two pendula have equal lengths I and have bobs of cqual mass m and both pendula are confined to move in the same plane, as shown in Fig. 27 (a) Show that the kinetic energy T and potential energy U are given by T="?[237 + + 2006, cos (6) – s)] U =-mg (2 cos + cc + cos ] Fig. 27 Assuming U= 0 at the top hanging point. (b) Considering the case of small oscillations (so that sin 0 = 0), show that the characteristic frequencies of the oscillation is given by (c) Obtain the normal mode for each frequency and describe its oscillation.