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A force of 400N stretches a string 2 meters. A mass of 50kg is attached to...

A force of 400N stretches a string 2 meters. A mass of 50kg is attached to the end of the spring and stretches the spring to a length of 4 meters. The medium the spring passes through creates a damping force numerically equal to half the instantaneous velocity. If the spring is initially released from equilibrium with upward velocity of 10 m/s.

a) Find the equation of motion.

b) Find the time at which the mass attains its extreme displacement from the equilibrium position.

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