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A block having a mass of 5 kg is suspended from a spring having a stiffness k = 200 N/m. If the block is pushed down with a velocity of 2 m/s from its equilibrium position. Determine the equation that describes the motion. What are the amplitude and the natural frequency of the vibration? Solve the differential equation for displacement as a function of time. Assume that positive displacement is downward.

Solution:

Given that the mass , spring constant , and the initial velocity The potential energy stored in the spring when the mass is at maximum displacement (amplitude A) equals the kinetic energy of the mass when it was released.

So,