an object weighing 4lb, when hung from the ceiling, stretches a spring by 6in at equilibrium. the mass is attached to a viscous damper with a damping constant of 1.5lbsec/ft and is set in motion from its equilibrium position with an upward velocity of 3in/sec. taking the downward direction as the positive direction, fin the displacement y(t) in ft of the system from the equilibrium position at any time > or = to 0. ( g=32ft/sec^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.