A 1-kg mass, when attached to a large spring, stretches the spring a distance of 4.9 m.
(a) Calculate the spring constant.
(b) The system is placed in a viscous medium that supplies a damping constant μ = 3 kg/s. The system is allowed to come to rest. Then the mass is displaced 1 m in the downward direction and given a sharp tap, imparting an instantaneous velocity of 1 m/s in the downward direction. Find the position of the mass as a function of time and plot the solution.
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