A 96 lbf weight stretches a spring 4ft in equilibrium. It is submitted to friction with damping coefficient y = 12lbf The weight is initially displaced 1 foot below equilibrium and given a downward velocity of 4ft/sec. Set up and solve the initial value problem modeling the displacement of the weight for t≥ 0. Note: Please use g = 32 as the acceleration due to gravity. sec

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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.