p2spring07_cut

# p2spring07_cut - Prelim 2 Math 293 show work 5 questions no...

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Prelim 2 Math 293 Spring 2007 show work, 5 questions no calculators, you need not simplify answers 1) A train moves on a track. The track has joints and other variations which repeat every 10 meters, and we will assume these to be sinusoidal. We model the vertical position y ( t ) of the freight car using my ±± + ky = f 0 sin( ωt ) . The mass m will depend on whether the car is loaded or empty. a) (5 points) What should we take for the value of ω , if the train runs at 20 meters per second? b) (5 points) The empty freight car has a mass of 20 000 kg. When loaded with an additional 80 000 kg load, the springs depress an additional . 02 meter. What values should we use for m and k in the equation of the loaded car? (Remember weight= mg , g = 9 . 8.) c) (5 points) The forced response which is observed under these conditions is y = . 003 sin( ωt ), i.e., the loaded car vibrates vertically with an amplitude of 3 millimeters. Find an expression for f 0 in terms of the other parameters. (You don’t have to simplify it, but if you want to check it, it ought to be

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## This note was uploaded on 01/21/2011 for the course MATH 2930 taught by Professor Terrell,r during the Spring '07 term at Cornell.

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p2spring07_cut - Prelim 2 Math 293 show work 5 questions no...

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