Show,by integration that the moment of inertia of a uniform thin rod AB of mass 3m and length 4a about an axis through one end and perpendicular to the plane of the rod, is 16ma2  The rod is free to rotate in a vertical plane about a smooth horizontal axis through its end A  Find i)The raduis of gyration of the rod about an axis through A ii)The period of small oscillations of the rod about its position of stable equilibrum iii)Hence determine the length of the equivalent simple pendulum

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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.