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quiz4soln

# quiz4soln - 530“" WW" MATH 2930 Summer 2809...

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Unformatted text preview: 530“" WW" MATH 2930 - Summer 2809 Quiz #4. — July 6, 2009 1. Find the appropriate form of a particular (trial) solution of the differential equation 3;” ~2y' +23; = e”: sin (E. Assuming that you can ﬁnd. the constants in your trial solution (you don’t have to), What is the general solution of the differential equation? a) 2. Consider the mass /spring system with m x 8, k m 2, operating freely and undamped. The differential equation that moclels a free mass—spring-dashpot system is méc' + cat + km m 0. (a) Solve this differential equation with the appropriate vaiues for the coeffi- cients. (b) If the system is now driven with the forcing function F(t) m F0 cos wt, what does as have to be for resonance to occur? ((1) Suppose we add a damping device, with c = 8. Is the system overdampeci, underdamped, or critically damped? (d) Without solving the new differential equation, sketch a typical curve rep- resenting the damping you identiﬁed in part (c). 8i+2x= O (’%{1+Q9© ...
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quiz4soln - 530“" WW" MATH 2930 Summer 2809...

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