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Unformatted text preview: Prelim 2 Math 2930 Spring 2011 show work, 5 problems, no calculators 1) (a) (4 points) Write your name and section number on your exam booklet. In parts (b) and (c) we consider the function of period 2 with f ( x ) = x on the interval- 2 , 2 , and f ( x ) = 0 for other points in [- , ]. (b) (8 points) Find the value f (6). (c) (8 points) Find the coefficient b 3 , of sin(3 x ) in the Fourier series of f . 2) The weight of a 1000 kg mass compresses a spring 9.8 millimeter. (a) (5 points) Tell why the spring constant k = 10 6 N/m. (b) (5 points) Write the Newton F = ma equation for frictionless un- forced oscillations of this system, in terms of the vertical displacement from equilibrium y ( t ), and verify that it can be rewritten as y 00 + 1000 y = 0. (c) (5 points) Write the general solution to the equation of part (b). (d) (5 points) Will the mass oscillate slower, or faster, than 29.30 cycles per second?...
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