5. After a mass weighing 10 pounds is attached to a 5-foot spring,the spring measures 7 feet. This mass is removed and replaced with another mass that weighs 8pounds. The entire system is placed in a medium that offers a damping force that is numerically equal to the instantaneous velocity. a. Find the equation of motion if the mass is initially released from a point 1/2 foot below the equilibrium position with a downward velocity of 1 ft/s. b. Express the equation of motion in the form x(t) = Ae sin[( )t ]

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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.