A machine of mass 500kg is mounted through four mounting pads that exhibit linear elasticity and viscous damping. In mounting the machine each pad was observed to undergo a compression of 10mm. When the machine was given a small vertical deflection and let go it was found to execute free damped vibrations such that it made 80 oscillations in 18 seconds. For this system find: i.          The stiffness of each mounting                                                                                 ii.       The damping coefficient of each mounting                                                  iii.   The minimum number of oscillations and time it will take for the amplitude of vibration to be reduced to 2%

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Free Damped Vibrations

Free vibration is a type of vibration in which the external force is removed after giving the initial displacement to a body/system. In other words, in this type of vibration, force is applied at the initial displacement of the system, and after the initial displacement, force is removed, and the system vibrates at the natural frequency.