A spring is such that a 2-lb weight stretches it 6 inches. There is a damping force present, with magnitude the same as the magnitude of the velocity. An impressed force (2sin8t) is acting on the spring. If at t = 0, the weight is released from a point of 3 inches below the equilibrium point, find its position for t > 0.

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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.