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hw17 - F t = 2 sin 3t lb(Given that g = 32ft/sec 2 Let u t...

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MATH 262 Homework 17 April 9, Spring 2010 Name: Section: NO CREDIT WILL BE GIVEN IF YOU EITHER SHOW YOUR ANSWERS TO OTHERS OR YOU COPY FROM OTHERS. THIS QUIZ SHOULD BE DONE BY YOURSELF. 1. (5 points) A mass weighting 8 lb stretches a spring 6 in. Suppose that the mass is displaced an additional 3 in. in the positive direction and then released. The mass is in a medium that exerts a viscous resistance of 4 lb when the mass has a velocity of 2 ft/sec. Assuming that the mass is acted on by an external force of
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Unformatted text preview: F ( t ) = 2 sin 3t lb. (Given that g = 32ft/sec 2 .) Let u ( t ) denote the displacement of the mass from its equilibrium position at time t , measured positive downward. Find a differential equation for u . 2. (5 points) Consider the spring-mass system whose motion is governed by y 00 + 2αy + y = 0. Determine all values of the positive constant α for which the system is (a) under-damped, (b) critically damped, and (c) over-damped....
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