Suppose that the spring mass system of Exercise is suspended in a viscous solution that dampens the motion according to R(υ) = −0.125υ. Furthermore, a machine is attached to the top of the spring that shakes the spring up and down harmonically with period T = 4s and amplitude A = 0.25 m. Assume that the spring is initially displaced 0.25 m downward from the spring-mass equilibrium by this driving force. Adjust the model in Exercise to satisfy these additional constraints.
In an experiment, a 5-kg mass is suspended from a spring. The displacement of the spring-mass equilibrium from the spring equilibrium is measured to be 75 cm. The mass is then displaced 36 cm upward from its spring-mass equilibrium and then given a sharp downward tap, imparting an instantaneous downward velocity of 0.45 m/s. Set up (but do not solve) the initial value problem that models this experiment. Assume no damping is present.
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