A coupled pendulum system is in a vertical plane (as shown in the fig. 2). Each rod is of mass m and length I and can freely oscillate about the point of suspension. The spring is attached at a length d from the points of suspensions. Write the equation of motion for both the rods and find the frequencies of normal modes. Find out the ratios of amplitudes of the two oscillators for exciting the normal modes.

A coupled pendulum system is in a vertical plane (as shown in the fig. 2). Each rod is of mass m and length I and can freely oscillate about the point of suspension. The spring is attached at a length d from the points of suspensions. Write the equation of motion for both the rods and find the frequencies of normal modes. Find out the ratios of amplitudes of the two oscillators for exciting the normal modes.