Consider the spring-mass system depicted in Figure 10.8.4. At t = 0, the mass is pulled down a distance 1 unit from equilibrium and released from rest. After 3 seconds, the mass is dealt an instantaneous blow that imparts five units of impulse in the upward direction. The initial-value problem governing the motion of the mass is d'y + 4y = -58(t – 3), dy (0) = 0, dt y(0) = 1, where 5 8 (t – 3) describes the impulsive force that acts on the mass at t = 3, and the positive y-direction is downward. Determine the motion of the mass for all t > 0. %3D Positive y- direction Impulsive force acts after 3 s Figure 10.8.4: A spring-mass system in which friction is neglected and the only external force acting on the system is an impulsive force that imparts 5 units of impulse at 1 = 3. wwww

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