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Exam _1_sol

# Exam _1_sol - 1 Exam#1 MAE 650:443 Vibration and Control...

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Unformatted text preview: 1 Exam #1. MAE 650:443 Vibration and Control Consider a simple freely Vibrating mass—spring-damper system. (a) Draw the ﬁ‘ee-bod§—diagra1n, and derive the governing equation. (b)Derive the characteristic equation for the system. ’ (c)Find the possible solutions to the characteristic equation as a function of g. I i (d) How the displacement with respect to time would look like for each case, i.e. under damped ,‘ over damped, and critical (draw). \‘W/ (l C! W [5‘ 21‘ : (HQ “ii (LAB/‘2‘ 1"“ “kt-“(1‘) f f; l j Y‘fx l § x L i»: Ada-’1 c 45 :m._-4)(g—U \$55.45} 4% 095+ if’XliCl K OC ’1 M ? 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[V r '“7 y A c Li (97 a i Q! , «a n (isxn'li favch K‘- . “If A ‘, r ‘ VGLVS (I) ﬁt [5 Ma 37/65?ka a/y/l/ediloo Wait” 0‘ L r .4 ,' a?" '1 e as the new €0F./\mitekrv\m g0: V0“ 3 I j: 1 My . : l V i p a, .p ,1 , q \[0\(~"{-":r‘(£ 0\CTS kt ’6 . i. 1' ’H'f‘ Ce aﬂii‘ <5i¢iftCZ/{‘4“r'i fO(”/0i(€ H“ J 7 L? ([5 I a, «ﬁx.» 5 a oyr'mm' e A H 1‘ ,_ {Lei w: I. ‘ f "a v/ 4': L h: 3 H4301 ENCle 7‘: [’L )“‘ M ii “(Gin 9' , ‘ v ‘I ;' I O V l/’ 5 ’L ‘J\« bidrr}; turf} ' The system shown below is deﬂected by x from the equilibrium position and is oscillating harmonically. Find the natural frequency. /~\ 35 v- m Q‘l'xﬂl’w“ \"Eb’vk‘x‘ﬂ Vafycll- 0‘] x- a "/lfl/ﬂ 5 -’7 Conseu‘xlo’lwo Su‘b (31" T: g at a ,L ’2, iii-191‘ F You have been asked to design a suspension system for a vehicle with the mass 500 kg. The vehicle and its suspension are modeled as a single degree-of—freedom oscillator. The customer wants the damped period to be ls,‘ and that the oscillation amplitude decays to 25% after the ﬁrst half-cycle. Find (a) the damping ratio (b) spring stiffness (c) damping coefﬁcient. m 35% j (a) 3:? i , M“ I 0 “’6” L“ 1 iii (La) {-3. d {Hts 24:; (C) C” I ) ﬂ ‘ Q” a at: <\ lot/“l (0’) 0 , ’ 0% {X ; KK‘MW, ":1 f j -M wwwwww _, 0M ‘3‘ " ‘ u 1 (L q"? {:mdqw =3 3 f 3'5 r "“i/ 7 1 (r Fly/‘- m‘ 1—; 6Jqu 5° .‘ 3 4.. _ v v.7... WWI,” { r" I " a f [L l )x , 15 a: L; I/W § —-. mg" g) N l r If s 5 2; g I I ,/5 / ﬁﬂ M wwwﬁwﬂﬂmm W} M“ O a [Ni-a: l ier’k it) E; V 9““? I? )r c. "’ 4"\ 5) C T: W. ‘1” C n'} (I) 1 ‘ “A “‘10:, I" L“) C 3 R ............ 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Exam _1_sol - 1 Exam#1 MAE 650:443 Vibration and Control...

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