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Q_3+Solutions+2011

Q_3+Solutions+2011 - RUTGERS University Mechanical&...

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Unformatted text preview: RUTGERS University - Mechanical & Aerospace Engineering Quiz#3: Vibration 21 October 2011 — 8:40 — 9:20 am Haym Benaroya - Closed BOOK/NOTES - Show All Work F 1. (4 points) For the force time-history graphed at left, set up all the equations and show all the steps sin I needed to use the method of convolution to find the Zero response x(t) for all time, 0 < t < 00, of a damped elsewhere oscillator with zero initial conditions. Results can be 1 left in integral form. Sketch what you' think the 0 n 21: response will look like. 1 $1402. f; fiscal/1WWI we WA 14m; out/W Mme/M fa wok cow'fi'ww Mug/Cf f - P 0<f<rri X/f)r/) F/f);/{'L>JL A W :/ZL fin”: exf%_]MW[{—LJ)- 0 Wrwflq These equations may be usefiJl: t 1 x(t) = f g(r)F(t — 1')d1: L [mwd eXPC—Cwn 1') Sinwdtr 4’ < 1] o 1 g(t) = mwd exp(—Cwn t) sinwdt = ———'Sz + zzwns + (0% Borel’s theorem: L‘1 [X (S)H (3)] = I: x(t —- r)h(r)dr 2. (6 points) For an underdamped oscillator forced by the unit step load u(t — to ), find the response v(t) for zero initial conditions using Laplace transforms. Write the equation of motion. Sketch the force. Show all steps but do not evaluate any integrals. Results can be left in integral form. 1L; "f to Uq’ @700» &'+ cal-U" “[1!” to) 72;;7/ W fin/1.74.4, m 7L‘ran574’l/M LS V/¢>[§7’+ awn-gr wfl j; (yr/MM») '31” '0 QM OZ/M({’toy: f (4/15 {)d’t Sf 00 "Sf ' 64wa -1 0’6 ’f 6 0/14— /, f .5 76° I «3139 $7) V8)? I v 3L3 g‘L‘fclJ’th‘TWJ— J UH) = 07" 3’ ° j i o a” A} bWfiM* ea 7w Z)09' wdl" o “(1‘4 ~50) dl’ :— 1 W o Maud f w a rt‘ffa‘éa') ‘f‘éméy T’é-“c ...
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