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In the absence of damping, the motion of a spring-mass system satisfies the initial value problem my?? + ky = 0, y(0) =

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In the absence of damping, the motion of a spring-mass system satisfies the initial value problem my?? + ky = 0, y(0) = a, y? (0) = b. (a) Show that the kinetic energy initially imparted to the mass is mb2?2 and that the potential energy initially stored in the spring is ka2?2, so that initially the total energy in the system is (ka2 + mb2)?2. (b) Solve the given initial value problem. (c) Using the solution in part (b), determine the total energy in the system at any time t. Your result should confirm the principle of conservation of energy for this system

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