This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: Your Name: T&AM 203 Prelim 1
Tuesday Sept 26, 2000 7:30 —— 9:00+ PM Draft, September 26, 2000 3 problems, 100 points, and 90+ minutes. Please follow these directions to ease grading and to maximize your score. a) No calculators, books or notes allowed. Two pages of formulas, from thenfront of the text, and a
blank page for tentative scrap work are provided at the back. Ask for extra scrap paper if you need
it. b) Full credit if 0 —>free body d1agrams<— are drawn whenever llnear or angular momentum balance 1s used; 2 correct vector notation is used, when appropriate; T——> any dimensions, coordinates, variables and base vectors that you add are clearly deﬁned;
:l: all signs and directions are well deﬁned with sketches and/ or words; —+ reasonable justiﬁcation, enough to distinguish an informed answer from a guess, is given;
3 you clearly state any reasonable assumptions if a problem seems wily W; 0 work is I ) neat7 II. ) clear, and
III.) well organized; 0 your answers are TIDILY REDUCED (Don’t leave simpliﬁable algebraic expressions); El your answers are boxed in; and >> unless otherwise stated, you will get full credit for, instead of doing a calculation, presenting Matlab
code that would generate the desired answer. To ease grading and save space, your Matlab code
can use shortcut notation like “(97 = 18” instead of, say, “theta7dot = 18”. c) Substantial partial credit if your answer is in terms of well deﬁned variables and you have not substi
tuted in the numerical values. Substantial partial credit if you reduce the problem toa clearly deﬁned
set of equations to solve. ' Problem 1: A
Problem 2: z 30
Problem 3: z 30 TOTAL: [100 1X40 pts) 1a) (15 pts) A mass m is connected to a spring k and launched from its static equilibrium position
at a speed of 110. It then oscillates bank and forth repeatedly crossing the equilibrium. How
much time passes from release until the mass moves through the equilibrium position for
the second time? (Answer in terms of some or all of m, k, and v0.) [Neglect gravity and friction] HX;0 ﬁT EQUlUMI’W ﬁ 0.0 / E = (I
W F5kﬂwwww...WWW—WM...“
__ W , é: mx=/KX :: 557’ MW IC‘b 1A5)~D (70%;; W52; “gngt (25% 74606 W6.) ’c ’5 5/ a (f? 92/0)= Yo X69: :E;/£}5m(ﬁ2)+ +F5coedft) ”ﬂ..~_umw~m._w.,_.~mwa .,. ., ... .. * M '. Xfijf0==7lfoﬂj [5:14.171 ﬁXﬂQﬂ/agsﬁ} 75rd”) M_ Megan: PM med pc[{).o :; Vonjmagfﬁ ~ m
alien?" J 75%40 Mk J? (£597?) 1b) (10 pts) For the mass above how far does the mass move from the launch position before it ﬁrst reverses its velocity? 1?ng lo») 7([E)= %F5M(J£»f) W66 vecocny M i=4)
,7: pasmox) coaespows 77)
7?—/€ ﬁmr’uwﬂé 0‘ MC moﬂou 1c) (15 pbs) A mass m = 1kg is held in place by a spring k = 1N/ in and dashpot c = 1 N/(m/ s). An oscillating force is applied of
F = Asin(At), with A = 1 N and A = 1/ s. After any initial transients have died down, how far does the mass go back and
forth (the distance from one extreme to the other)? W4F=ﬂsinéfl a; ,,... m—
313? Ear—:5? ,, ’ 1‘
3 ﬂ 1: (m: x B¢ajf+65m
6M6” W ”In. a o [Ll/57.? 86am)? i1‘ way/<5
(3:01 f:;—(Sih£\ +6800} t+C§iﬂﬁ) fCBcaJ'f‘f“ CS‘Mé)—737W6 ' "‘ l‘ 't i . a "t '1“ Ban“ {—mef) '4‘". ’ (“Bcajt—CS'Inf) +<JB£Int+ [r J ) gﬂf ¥rﬂﬂld€ flartloa'ifdme]
(allelj'i SibQ X’ («3152 , 1‘6qu Eﬂza
~B +C +B=0
96:0
—c ’13 +<c1
=5 8:“!
=7 ><=—cos(t) .u 2)(30 pts) A system of three masses, four springs, and one damper are connected as shown. Assume that
all the springs are relaxed when 33,1 = :63 = ID = 0. Given 1:1, 1:3, k3, k4, c1, mA, mg, mp, 1.4,
323,351), 55,4, i3, and ip, ﬁnd the acceleration of mass B, $3 = 51531. 3) (30 pts) In three—dimensional space with no gravity 3 particle with m = 3 kgAat A is pulled by three strings which pass through points
B, C, and D respectively. The acceleration is known to be g = (ai) m/s2 Where a is not yet known. The tension in AB is
4N The position vectors of B, C, and D relative to A are given in the ﬁrst few lines of code below. Complete the code to ﬁnd a. The last lineshould read a = . . . with a being assigned to the acceleration in the i direction.
F 9.0 O m
J .J 'ﬂ/ﬂ
draiﬁ+$c+$D=MG£3QC 4 Te {1‘ ’I‘T‘el= TN 9W ___, ’1 .3 ’\ .5 ; ’l
Def/M6 wr reams 73. 7525) ESE/1c, To 7920
Oeﬁwﬁgﬁn mas. 0:23 Egg/ma); ‘ 77/5“ 7335+ Elﬁn/lo =01; ”9 M“ “ﬁﬁﬁmmmmrj'ajar
g) FEEL—t 77230 fag: ~ 77538
[1‘4 q {1’
105_1]1T% :’TB jib Z a. MATLAB script file to find 3 tensions m =3; a =[123]’;
rAB= [235]';
IAC = [3 4 2]’;
rAD = [ 1 1 113 uAB = rAB/norm(rAB); 7. norm gives vector magnitude “A You write the code below (however many lines you need).
”I. Don’t copy any of the numbers above. "A Don’t do any arithmetic on the side. U AC: rAC/normO/‘ld :1
m0. rM/nomwo) ) I b: [m o 01‘,
Tb: 45 PsTbkwﬁﬂj
 A= [use mo 4213
res: mm 01». rCSC'b)j ...
View
Full Document
 Spring '08
 RUINA

Click to edit the document details