EXAM2_2007.pdf - ME/AE 455 MB/AESSS CE 51 Student Name Oct...

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Unformatted text preview: ME/AE 455 MB/AESSS CE 51 Student Name: Oct. 29, 2007 1. (50 points) Using the impulse response method (the convolution integral method), compute the response of the system whose equation of motion is obtained as 56 +21: +9x = 6(1‘ —1)+25(t — 2) subjected to the initial conditions x(0) = 0.1 m and J'c(0) = 2.1 m/sec.5(t)is a Dirac delta (impulse) function. Response in all time intervals is to be computed. Check if you solution is satisfied at t=0. All units are in SI. Hint: total solution = homogenous solution + particular solution. __ L _ L _ 33 m: l L:2_ __ KJ n:_k:____3r-cll3’ -—.——_._:~:_~_O ‘Ls t5“ LC 5 {M M ? 4'1“ ZJ‘LJQ (Ste. p_1L.) ~Twn+ ”Jul: w“ (”XL =2_8’5 rat‘s "Mai-H:- J. c. smicud++¢\ #flcofime -——-_——"““‘1 + “d '71 1‘ *‘ ’LHJA .., 1. d. A: whjflilfitgffifil ; 0-48 M) £5: ax 0 \‘Z. r' ./ /’w 2__ Kin-{*KUJA’LG O \_7.r ‘ d‘ _ V . :1.18 2.1””; / 0-! ‘4‘ L334; 0.1-) t—Ir 20.4—8 a ~3- \2- +0. ‘ "A“ 3 mm A a “flu-I'd- -- - __ “ + _ Hr): __ e; gzmul + lmpfibc. “$56.: mq4g1+Kq—'—s§(l">qé “quad d ‘ ...o.'3‘1A3(t-I) Spa-W 7-) 1PH\= "— 5?- Stall-33(lqfi ' 2-33 -Ra-t) :0-2‘53 a sewn—sew“) -(+—?_\ 3_g(+-1\ $19“): 3:. e“ Saki-83 (Jun) 1 28's _ - 3 ‘3 0-?! ‘1“. 2 gm t1.83(+‘2'\) ‘tclzzt SoliHcy-x: '1H\.—.'?LhL—H+ 1‘, H3 §(+~\\ +19“ \EH‘Z) | 2. : CML: ! anc": Q-\ N\ d1 ' ____r\(,d\ =Z-\ MIML d+ l Fall 2007 c. Cetinkaya 2 of 3 ME/AE 455 ME/AESSS CE 5] Student Name: Oct. 29, 2007 2. [50 points] The equation of motion of a forced system is given as 55 + 56+ 9x = e" . All initial conditions are zero (that is, at t=0, the system is at rest). All units are in 31. 2.3 [20 points] Using the La lace transform method, compute the response of the system in Laplace (5) domain, (“Mt it ‘3 namely, X(s) = ? ~l‘ i irks cling u l“ X(s}—— _.__L.___. (SH) (sis-+3) 2.1) [30 points] Using the inverse La lace transform method, compute the response of the system in time (1‘) domain, namely, x(t) = ? Hint: Use partial fiactions expansion and the Laplace table. E:3 PW“ 45mm 5mm“, ><m= il-l- ‘ f l 1L%}='_L(3fi:‘ __._ ._ 07:“ s \ = s a: " yawn: +- We \ - L 3 Sill ,‘ $z+$+3 j 4 BED + j (S+\?+ 35 l rdlchlg S‘HIL‘ /2_ 344]; __ [I1 remit 2'}. ($43 +35 LSi'DLi-gé S+\\l+§§_ ‘\ 2.. H 2 ‘1 3‘53 o-F—tr «3-35 t k] 4‘ 4‘ H7. (5 _. _ ,_ _ -:. J— (a —- a Loafing-4:) -l- .1— e. 5““ ”Bi-"£3 a wflw 35 1‘ 62:”; v—! 2. 6'1"}. “'1 E5 1 '3'; rolgfi’s H W 3 [L1 rdLLfit 755 Fall 2007 c. Cetinkaya 3 of 3 ...
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  • Fall '10
  • Centinkaya
  • Impulse response, Dirac delta function, La lace transform, lace transform method

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