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Unformatted text preview: Name: Sold/47% g Perm No.2 Section Time : Math 5A  Midterm 1 January 28, 2098
Instructions: 9 This exam consists of 4 problems worth 10 points each, for EL total of til) possible points, a You must show all your work and fully justify your answers in order to recieve full
credit Please indicate your answers Clearly by placing a BOX around them. You may leave your answers in unsimpliﬁed form. Partial credit will be awarded for work that
is relevant and correct. 9 No books, calculators or other devices are allowed, You may use one 3” x 5” notecard. 9 BOX YOUR FINAL ANSWERS Write your answers and work on the test itself, in
the space alottecl You may attach additional pages if necessary 1‘ Solve the énitiaé value problem
y” + 431’ + 8y = 0, :y(0) = 2, W1) = "6
‘ '1
T "\' H r 4: 8 =1 B r" : "Ll tJlkBL L ~=~ ~Zizl'i :5: K5 2.: {351% (:1 aengH clgmclmv Kym": Eta/(I C\ (ﬁg?) “1“ Ca, Sin/IQ}
"r" f (gr : C1 “—3 1.
W933“ wlﬂe”1t(ck L%‘S(1H+ (19“th + ﬁﬂlt(b1C\€1n(1t]+1€1 Cmﬁzm) WW3: "1C‘+ lcl 2 ~ (g 1'0 2. (a) Find the general solution of the homogeneous equation y” —— 4g + 4y :2 0‘ r1~Hr+Htﬁ>
(“lTL 1“ ‘93
Y‘ T. l (“Lo WM" R. {Kg/Vi}— 2'&, t 2:.
. . . 6
i3 Flnd the General soiumou of the non—homo enoous oc uatlon ‘1” — 41’ + 41 m —
o J J J \jCLVEOJK’CW 9% PUJ‘ OJMQ/‘Q'W‘X
it. t 621: L5\9'I ngﬁ‘ +\}7_ {ﬁz gt: '6’ L51:
E ’.. “Lt lb, "M:
Lj‘ ~19, \jz~(¢2£+\3€ 3 (a) Find the general solution of the homogeneous equation y” w Gy’ + 5y = 0. ercori— 5:“ 0
0r”..— SUQr» U: C) rr—SE\ t. 1:; Find the enera} solution of the nonhomogeneous equation y” — Gy’ + 5y m 12te“‘“1
g waé «ﬁre/rmmdl Wﬁﬁnm‘ﬁ 1
(if/‘9” 3g __ W: wag.“
U36 = “(At+ﬁ)eft+ /\ 9ft" :1 (HAtH‘c—E} aft
3;:  LAt++xmét+ h Heft
3 (At "2A +1515“: m" w: wm'ﬁAtwa + w— eeAtWW SQAtHﬁﬂ fit :: \1teﬁ't
.... .. __ WAS—m.
_:> FLA11. wwAwm—l
Kle~ge~=e meat. 3;
m, 3, it. Consider a niass—spiing, system with a, 2 kg mess attached to the enci of the spring A
force of 196 N is required to pull the mass 0 2 in from its equilibrium position. The mass is then released with initial velocity :c’(0) m —0 Tm/s, and we observe that the
mass reaches its maximum speed preciseiy when it passes back though the equiiibrinni
position. (a) Show that there cannot be any damping (ie, 1) m U) mx"+bx‘+\¢¥ :22. C). was», m was Fm Wm m Qa‘u‘\i_\ior0.LJAA theatre“) x: 0. (items. semi G. Wyumumn o59x‘ +1“:
task—aygk") X,‘ m o“ reXanVL mhwum (MMMMQ M "WM/cg. K”—:_b 6&— mm L“§W,
$3 \on‘ “rm—E, KeirUL m vakeﬁt~1 \d knee—Q (b) Determine the spring constant is, and ﬁnd the empiitude A of' the motion of the
mess (You may assume there is no damping, even if you cannot do past (a)‘) almi‘+k¥~=—Q, le‘eQixao Ernie—x. ws=J“/M=W =7: [m N n em. “0
x: g was (Tet) + (L $w Hit) \ .‘l 6‘8] XtﬂﬁzaL M
i (“”7 Q Wino}: m}?
woo: ”3‘L13\m(.¥ti+ "}(,LCX)% (Ir—e} “W Waxy/e Wong/e >A=m
0 15 :3: ...
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 Winter '07
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