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Unformatted text preview: Fall 2011 AAE 340 — Dynamics and Vibrations Exam I Sohdw'onia Please read the problems carefully.
Write clearly and use diagrams when necessary. ( 35 points) 1. Below a small block B moves on the surface of a plate. The axis denoted 52 is normal to the plate; the axis passes through the plate at point Q. The [32 axis rotates about the inertial axis
Q] at the constant rate 7 = Q rad/s. Block B is ﬁxed on a rod that pivots on the plate surface about point Q. A . , ' __ . A
'Deifne “TOW b c ¢b°1 bl Q' (a) Use 13,. as the working frame and derive an expression for gZQB. % a, (b) Is this a generic acceleration? Why or whyA not? = Rc.= R0¢b3+ Rsasbn ‘3; ~_QB _g[q._p+%—bxf~ =~R¢3$¢b3+R¢c¢b1 —R7rc¢b9~ _QB v + waV =(—Rq§s¢— “R.C¢)b3
+(Ra5ccp R65 soot»
+(— R?c¢+RY¢S¢§b/\Aa +Rif¢5¢bg” Riga/1553 A“;B  (Rib'cgs— Ra's “sub. +(—R¥0¢+aR mas) 9;. + [ REDS¢— Rab “'+i‘lcqs]b3 not mmtTc—ﬁwﬁn é: % ( 30 points) 2. In the system below, a particle P of mass m can move in a vertical plane with a spring and a
dashpot attached. The location of the particle with respect to the ceiling is described by A . (a) Set up the problem: deﬁne the variable(s) of interest, FBD, and the force models.
(b) Derive the EOM in terms of xi. Deﬁne. \«(o unsmmct [009% 076 SPVMQ"
S ﬂoath'on 0? s+aﬁe 6%W'Ubr'“m . . . .
g l i ParHale, roazHon relwhm 40 8753/70 ﬂaw br'W’L A particle. Locarh'on ralcchW~lo aca'Qn’n% 94% + of» + “ELK(Ale; =r'm}: é;
mX+Q>l+ ‘k A = “Kai“MO ” Q. :2 +£ﬂo
la+m>t+jgx ?r WC‘ (35 points) 3. Assume that the system in problem 2 has an EOM of the following form:
2.: + pi + q/i = f
where p, q, f are all constants; A in means . (a) If the damping ratio is 0.5 and the damped frequency is J3 rad/sec, determine p, q, and
the characteristic roots. Compute the damping time constant and the cycle time. (b) Let 2(0) = +3 met, 2(1) = J3 met / sec, and f = 12 Determine the total response, that
is, the complete solution It(z‘) in amplitude, phase angle form. (0) Sketch the response on the next page. There should be three curves in your sketch.
Label each curve; include the equation corresponding to each curve. Add and label the time constant and the cycle time. (d) Sketch the phase curve. T=lscc
——> ’1?=3.(pa7(p 5m . 2 . .
’C’ tune (sec) Vague, Phase Plot ...
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 Fall '09
 HOWELL

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