In the figure, a disk-shaped wheel of mass M and radius R rolls without slipping on a circular platform of radius 2L+R. The wheel is attached by a torsion spring to a pendulum of length 2L of mass m and moves with this pendulum. a) Derive the differential equation for the motion of the system given here. b) Find the natural frequency of the free motion of the system. L=2 [m], R= 0,5 [m], m=5 [kg], M= 65[kg], kb= 165 [Nm/rad] Note: There is no friction in this system

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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.