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Midterm 1 - MECH 330 — Machine Dynamics I Fall Term 2013...

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Unformatted text preview: MECH 330 — Machine Dynamics I Fall Term 2013 Question #1: [20%] // L0 A simple pendulum is fpund to freely_vibrate at frequency pf 0.5 Hz in a vacuum and 0.45 Hz in a viscous {iii—El- medium. Fincl the damging c0nsta_11t__ of the bob in the Viscous fluid given that the mass of the bob of the pendulum is 1 kg and neglect all other damping. 7:] — 7.131 {0-1453 ? OHM n L/ _____._._..’-—~1 ’ a. -‘ g. 'l (My: 3/" “i z 1;. [0.3) :; Page 2 of 9 MECI—I 330 — Machine Dynamics Fall Term 2013 2,01" Question #2: [30%] /Z l The viseeusl-y damped system in the figure has aspring constant k =5;000 mass m t ‘2' kg‘ and m - logarithmic decrement of 2.0. If the system is given an initial velocity of 10 E and no initial low? : Xe S displacement (from equilibrium), determine the maximum displacement of the system. [mm = -l\><.- <>2 "a 2mm I9 l 7“ “_\ r A L : : 11/17 _ _ LU": : : lift: - l 9V > T4! — O .7 f-— y I _ (If: g ‘ d 0530?? :7 (elf C: i'afimmm " 0303?} 50w“ J (, i _ ‘H ‘0 C: 7HM l-j/j/ Aft/3} 70-1; pr(£ NEJ (“was Myer: £57 r}j._;p~£21-p,\1 m("~+’f_l_£ Y I: - igbmfg-‘fll twolél CM!" 'I'gif T FfiQ/f/ ' I A. is}: r: : 0.91% ‘4 1}fo i1 ,. f A f ‘ mm 1:1 ’ ><lia "‘t’mcm’l s: (lamb, JC ’3” a ? l K _ >408; / A J: W J “(I f , ye , l “303nm — l Page 4 of9 '") 2/ MECH 330 7 Machine Dynamics 2 Fall Term 2013 'Question #3: [25%] A metal block, placed on horizontal surface, is attached to a Spring and is given an initial displacement of '22 cm fr'csm the unstretched spring position. It is found that the tiine period of motion is Ill-.5 s and that the amplitude reduces by 4 cm in each cycle. T: l 6', Find: _ [hm Cr pt”. ((6? {The coefficient of friction between the metal block and the surface. ‘ 45? The niiifiher of cycles of motion executed by the block before it stops. (0) The firTalposition of the block. 5: 316m: N“ Page 6 of 9 MECH 330 — Machine Dynamics Fall Term 2013 Page 7 of9 MECH 330 7 Machine Dynamics Question #4: [25%] {5’ Fall Term 2013 Consider the system in the figure and express your answers in terms of m,l,k,cand the diSplacement 3'0)- Find: (a) The equation of motion. (b) The natural frequency of the system. 1?),in 2 L15“ ,3“ Uniform bar, mass m l Page 8 of9 ...
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