When a 40-kg machine is placed on an elastic foundation, its free vibrations appear to decay exponentially with a frequency of 91.7 rad/s. When a 60-kg machine is placed on the same foundation, the frequency of the exponentially decaying oscillations is 75.5 rad/s. Determine the equivalent stiffness and equivalent viscous damping coefficient for the foundation.

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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.