Under mind control of the horrifically evil villain Apocalypse, Magneto uses his

Question

Under mind control of the horrifically evil villain Apocalypse, Magneto uses his mutant power to magnetically construct a gigantic spring. He welds one end to the ceiling of the lobby of the X-mansion and the other end to Dr. Xavier, while simultaneously Storm creates wind resistance that damps Xavier's motion with a force of 30 lb when Xavier's velocity is 5 ft/sec. The spring is so strong that it would only be extended 6 in if the 160 lb Xavier were attached to it and motionless. Initially Xavier is released from static equilibrium with a velocity of 3 ft/sec downward. However, Jean Grey attempts to thwart Apocalypse by using her telekinetic power to impart a force of -2 sin t lb on Xavier. Set up, but do not salve, an initial value problem whose solution is the displacement of Xavier from static equilibrium at time t. Is the matron of Xavier overdamped, underdamped, critically damped, or undamped?

Explanation / Answer

Ans b) motion will be overdamped because some power to impact a force is being applied which sinusoidal in nature so it will be continue in oscillation motion.

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