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quiz15_Solution

quiz15_Solution - r B=-5 At6"\$t\t)=a-ts'^ I A= H1 6=h...

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Math 242, Spring }OLL Quiz 15 Name:.L?.1.t1.t9.d ..... i9' L. (L4 points) Consider a forced mass-spring-dashpot system with equation r"+2x'*br-2cos(at). Find the amplitude C(c,.') of steady periodic forced oscillations with frequency cl, and find exact value of the practical resonance frequency cl, if any exists. X; = -Arltr>,'t - b"25inort - f,t^lZrpsul+ - S-L6l;1,^it - f,{t^rSir,r^rt+ 36c. [osc., t t 5A <oso f, tS SSint^i* ' &' {oSQ* A ^ *(s-"r) + lr; ' S.l - a- ls--' wsw* :\ - A,"rL * e,M t5A = 2 ra g'rr\_ 'r \- / s-wt s\,r,o.[:]-tr,r.-p.A^,+sb=c
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Unformatted text preview: r B= -5 At6-"\$t\t})=a-ts-'^,) I A= H1 6=h, t'cr,)=1|ffi= C [u) = [a (*-6,;'r \ = a.tl) (rr-5'zt,rT;- b"'- R, --to (.,r- r) t) ** &rtS = O c _ -r.rfi;; '1,4" -T = xs\$)=hcl+\= Et [U ,uf* * .'ri',,r*) l) f,f= \$Us.,l{ t 6sh'"rt kl= - Nt^lsint,t + B'r r^ost''rl =-r!3 = -t je4 0 r'L +=\-(Not" {^-t &s.;t I s'"^t &'*< tff?t i^ X+(+l ,Jx urt u ) i.q* t"t'y es- 6,J+t^r't s'(s-d* As- 6 hl \( r), tas - e^'+of^ c(E)--AIS-D? 15 ' 66+cc1 (rs- 6ru'* r)\'= gro,c"tir,ot foono^trc [ttfltu*" - {1 C("\ ./.*-\ Cr,rt4(' 2-trfS - 18+J...
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