Suppose that the spring mass system of Exercise is suspended in a viscous solution that dampens the motion according to R(υ) = −0.05υ. Furthermore, a machine is attached to the top of the spring that shakes the spring up and down harmonically with period T = 2 s and amplitude A = 0.5 m. Assume that the spring is initially displaced 0.5 m upward from the spring-mass equilibrium by this driving force. Adjust the model in Exercise to satisfy these additional constraints.
In an experiment, a 2-kg mass is suspended from a spring. The displacement of the spring-mass equilibrium from the spring equilibrium is measured to be 50 cm. If the mass is then displaced 12 cm downward from its spring-mass equilibrium and released from rest, set up (but do not solve) the initial value problem that models this experiment. Assume no damping is present.
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