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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—springdashpot
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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 Spring '07
 TERRELL,R

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