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plugin-ch5soln

plugin-ch5soln - No calculator Closed book note Open...

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No calculator, Closed book & note' Open Laplace transform table tlath 245 Chapter 5 Test (l April2009) Spring 2009 Please check your discussion section: n llam n L2pm n lpm So/rtu'eu Prob. 1. (15nts) Write the g(t): function ( ' t t ' j tr-tl' I e-2tt-:l g(r) (defined for 0 < r < oo ) using the step functions. 0 < r < 1 l < t < 3 t > 3 0 @ @ o l 3 @ , t f i < g : @ t ? s : ftn = [l -,urt-l)] czl + [ CI rt- {J - 4ttt-31] rt - r)t+,lr tt-3)az"-'V Prob. 2. (15pts) Sketch the tunction f (t) = (t -2)u(t -1)-2(t -3)u(t -3) for t > 0 . f (t) 0 ; o ! t < 4 Jt*t =-o fltt= t-2 Jtt) = t-7-2,.<4)
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Prob.3. (lspts) Find the inverse Laplace transform of the function F(s) = '-r^'9t *!), s ' + 2 s + 1 0 Zs+l 2(s+{)-{ S+{ | 3 = - - . _ . . - = Z - - - - : - _ - _ - : ?4x|o - (s+'114* q (stt)'+ 3' 3 tstrla3L f t{ fr,, | = fl(t- +J f 21rc,,s3t - | a*r ^r. lt +t- 4 = {Jrt-+) A(t-+)l zrss(t-q*{ sm3(t-+)t 4 Prob.4. (20pts: l0pts/ea) Find the Laplace transform of each of the following functions: (a) f (r) = tsin2r . $s{rnl :***trn,ztJ= -*(d4) = #A-7, = 6sts-, I (b) S(r) = e'6(t - 5) Jtf,.,I =f f Ect-s{r*s_{ = 6ttlr*,-l 3{s-'t)tl=,= ant-"/4 AK. $ {lrui = J?.". [rt-t-) dr =
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Prob. 5. (20pts) Using the Laplace transform method, find the solution of the initial value problem:
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