38–4.42 Determine the amplitude of steady-state vibration for the systems shown in Figures P4.38 through P4.42. Use the indicated generalized coordinate.

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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.