a coupled pendulum system is in vertical plane as shown.each rod of mass m and length l and can freely oscillate about point of suspensions.write equation of motion for both the rods and find frequencies of normal modes.find out ratios of amplitudes of the two oscillators for exciting normal modes

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Free undamped vibrations

Whenever an object/system displaces in either side of its equilibrium position with the help of an external/internal means, then the object/system moves regularly or randomly on both sides of its equilibrium position. This motion is called vibration. Generally, there are three types of vibration: longitudinal vibration, transverse vibration, and torsional vibration.