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p2spring09

# p2spring09 - Prelim 2 Math 2930 show work 6 problems no...

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Prelim 2 Math 2930 Spring 2009 show work, 6 problems, no calculators 1a) (4 points) Write your name and section number at the top of this page. 1b) (16 points) Solve x + x + 3 x - 5 x = 29 e - t + 30. You are told that one solution of the homogeneous equation is x 1 ( t ) = e t . 1

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2) Consider the equation y + 81 y = 10 cos(11 t ). a) (8 points) Find a number a so that one solution is a (cos(11 t ) + cos(9 t )). b) (8 points) Find numbers b and c to express cos(11 t ) + cos(9 t ) in the form of an AM signal cos(11 t ) + cos(9 t ) = b cos( ct ) cos(10 t ) and sketch a graph of it to illustrate the term “Amplitude Modulation”. 2
3) A mechanical system with a lot of friction can sometimes be modeled as though it has a shock absorber but no spring. Suppose a box having mass m slides across the rough floor of a moving truck according to my + cy = f ( t ) Here y ( t ) represents the distance of the box from the side of the truck, and the applied force f ( t ) is due to the sideways lurching. Of course c > 0 for the friction, and we ignore any motion front-and-back.

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p2spring09 - Prelim 2 Math 2930 show work 6 problems no...

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