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Unformatted text preview: M427K (Unique number 55325 )
In class exam A Oct 26 2010 Name (PLEASE USE BLOCK LETTERS):
Student EID Number: —————_—_____—_—_—____—__—— Please show all your work and describe your reasoning. Indicate which method you are using to receive partial credit. NO PARTIAL CREDIT FOR
STREAMS OF FORMULAS WITHOUT EXPLANATION BOX YOUR FINAL ANSWER Start working in the page and continue in the back. If you need extra pages, feel free to attach them but put an indication that there is a break of continuity. Try to be as neat
as possible. No books, calculators or notes allowed. In all the problems, the independent variable is m art and the dependent variable is
y. Unless a method of solution is Speciﬁed, you can use any correct method. Extra credit will be given by solving a problem by different methods (if both solutions are correct). A general solution in the form F(m, y) 2 C is acceptable When solving the equation
for y is too complicated. M
Score Problem 1
Problem 2
Problem 3 Problem 4 Problem 1 (20 points) 1) Use the method of undetermined coefﬁcients to ﬁnd a
particular solution of the equation y(4) — 81g 2 3003(3t) 2) Write the general solution of the equation in part 1) w Th2 MAS" 0‘? MM; wwxoecrtljiml¥c «MWGX
W i% Mal i'E/t‘ Hal/L02, \Am Ma, (2%th when oﬁ m Jew/n ,2
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3 Problem 2 (20 points)
Solve the initial value problem y”  21/ + 4y = 0; 11(0) = 1;y’(0) = 2 using Laplace transform.
Partial credit will be assigned by solving the the problem by any other method. Also,
extra credit will be assigned by solving it by Laplace’s method and another method. WM? Yaﬂaa TFOWLZ: @«m (A >03 t \1 > (AZ—QLJAOY ~i ‘2 O
i an ==> {on = #— 352%“? (AH) +3 E M gig/L walk/wok of. Jc 1?
“w at m Mm 176) s 6 {6; 601% H+Cawlfi+lkm Problem 3 (20 points) A spring is stretched 10 cm by a force of 3 Newtons. The
mass of 2 Kg is hung from the spring and is also attached to a viscous damper which exerts
a force of 3 Newtons when the velocity of the mass is 5 m/ sec. The mass is pulled down 5
cm below its equilibrium position and released with no initial velocity. 1) Write down a differential equation describing the problem. Make explicit the units
of all the terms and make sure that the units match. 2) Find the general solution of the equation in 1). 3) Determine the position of the mass for all time. The ﬁrst sentence in your solution should be a line identifying all the
variables and the units. Make sure that the equation has units that match. W m WE m haze/us m {Wide/v3, ) bdocpoums ”1(0) = 906
Ag'LO) = o
m moo/(E 0:; W chmmciﬁhc WMWQQ m
—3 i V/JQ/mx/
fa: ~ 20 CL ’ 0053 r— v Clio?”
962/ _ 2 = o
Ci<’3/510>+ C; '20 “0 C2 Mai/3W Problem 4 (20 points)
For each of the following equations ﬁnd the general solution. M427K (Unique number 55325 )
In class exam B Oct 26 2010 Name (PLEASE USE BLOCK LETTERS):
Student EID Number: Please show all your work and describe your reasoning. Indicate which method you are using to receive partial credit. NO PARTIAL CREDIT FOR
STREAMS OF FORMULAS WITHOUT EXPLANATION BOX YOUR FINAL ANSWER Start working in the page and continue in the back. If you need extra pages, feel free
to attach them but put an indication that there is a break of continuity. Try to be as neat
as possible. No books, calculators or notes allowed. In all the problems, the independent variable is :L' ort and the dependent variable is
y. Unless a method of solution is speciﬁed, you can use any correct method. Extra credit
will be given by solving a problem by different methods (if both solutions are correct). A general solution in the form F(m,y) = C is acceptable when solving the equation
for y is too complicated. Score Problem 1 Problem 2 Problem 3 Problem 4 Problem 1 (20 points)
For each of the following equations ﬁnd the general solution. (1) y’ = 9(8 ~ W3
(2) y’ + (3/75)?! = t2
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I Wa oak/walla ”gm’ﬂfrllvﬂﬂd‘ﬁ
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/ 4.3; : €02 C
.16" / Problem 2 (20 points) 1) Use the method of undetermined coeﬁicients to ﬁnd a
particular solution of the equation y(4) — 16y 2: 2cos(2t)
2) Write the general solution of the equation in part 1)
® m Wag/(g of M alumna [ZN/Adm WWMAQ W ’52 M ﬂu
WM boo/Q favov window Whom 036m ﬁrm/Vb Harm A=~Aié WOC
//H W: iv W a M at / Problem 3 (20 points)
Solve the initial value problem 21” — 42/ + y = 0; 21(0) = 1;y’(0) = 0 using Laplace transform. Partial credit will be assigned by solving the the problem by any other method. Also,
extra credit will be assigned by solving it by Laplace’ 8 method and another method (AZ—WHQ—V— "‘24”: :71} M _ 54:2” 7.
1; 67’ f3 (FL (5,72)ng E @792) "3 \fajzvmj WU} imf #60114" 13; Etta/119413 Ha? BMVUEHE
._:_,./——’/% Problem 4 (20 points) A spring is stretched 10 cm by a force of 4 Newtons. A mass
of 4 Kg is hung from the spring and is also attached to a viscous damper which exerts a
force of 3 Newtons when the velocity of the mass is 5 m/sec. The mass is pulled down 5
cm below its equilibrium position and released with no initial velocity. 1) Write down a differential equation describing the problem. Make explicit the units
of all the terms and make sure that the units match. 2) Find the general solution of the equation in 1).
3) Determine the position of the mass for all time. The ﬁrst sentence in your solution should be a line identifying all the
variables and the units. Make sure that the equation has units that match. MM m Wmmtwjéeloayam
WM gamm 7% W Mam? do {a : LAN/hm = ¥0N/rm
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'2 F mV/gcﬂ/ M427K (Unique number 55340) )
In class exam A Oct 26 2010 Name (PLEASE USE BLOCK LETTERS):
Student EID Number: “EM.— Please show all your work and describe your reasoning. Indicate which method you are using to receive partial credit. NO PARTIAL CREDIT FOR
STREAMS OF FORMULAS WITHOUT EXPLANATION BOX YOUR FINAL ANSWER Start working in the page and continue in the back. If you need extra pages, feel free to attach them but put an indication that there is a break of continuity. ”ﬂy to be as neat
as possible. No books, calculators or notes allowed. In all the problems, the independent variable is LL‘ art and the dependent variable is
y. Unless a method of solution is speciﬁed, you can use any correct method. Extra credit Will be given by solving a problem by diﬁerent methods (if both solutions are correct). A general solution in the form F(m, y) = C is acceptable When solving the equation
for y is too complicated. ME Score Problem 1
Problem 2
Problem 3 Problem 4 Problem 1 (20 points)
Solve the initial value problem 1/”  61/ + 9y = 0; y(0) = 1; y’(0) =1 using Laplace transform.
Partial credit will be assigned by solving the the problem by any other method. Also,
extra credit will be assigned by solving it by Laplace’s method and another method. jag/wit fw.7/1WQKWM (£4341)
M’[email protected]ﬁ(—~g+5=©
g? 3AA): 4"; = ”4/3 ‘2 AZ/MH’ (#3)? w 3)2 TQM/(ﬂ; MAJ/£2193 :ﬂaJ/L /
‘ 3:62} Problem 2 (20 points) 1) Use the method of undetermined coefﬁcients to ﬁnd a
particular solution of the equation 74(4) — 2y(2) + y = 2et 2) Write the general solution of the equation in part 1) Q) m We at m mm W W :El M; Wt. 92. Problem 3 (20 points) Use the method of variation of parameters to ﬁnd the general
solution of the equation tzy" — 2y 2 3t2 knowing that y1(t) = t2, y2(t) = t‘1 are solutions of the homogeneous equation. We OUVLCQL kg t2 4v amaﬁm émtw U? ”(f I! MN ﬂ ’
M 13 Ajﬂbévz/QAkik\
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Mg , g é: M2~7€ 3 Problem 4 (20 points) A mass of 100K gr. stretches a spring 5m when you hang the mass from the spring. Suppose that the mass is also attached to a damper of constant
400Newton —— 366/ cm. If the mass is pulled 2m and then released without initial velocity,
ﬁnd its position as a function of time. (Use the acceleration of gravity 10m/sec‘2.) MWWW/M [email protected])&[gﬁammé{
Aecanaégm m [771% CWle ye: ng/V/gm=/9é N/m
WW ﬁgoN = {06 kg 69,8 ”AZ in W WWW?
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xf’m) :0 2% W) : 6.217% mama amazmwmﬂg M427K (Unique number 55340) )
In class exam B Oct 26 2010 Name (PLEASE USE BLOCK LETTERS):
Student EID Number: Please show all your work and describe your reasoning. Indicate which method you are using to receive partial credit. NO PARTIAL CREDIT FOR
STREAMS OF FORMULAS WITHOUT EXPLANATION BOX YOUR FINAL ANSWER Start working in the page and continue in the back. If you need extra pages, feel free
to attach them but put an indication that there is a break of continuity. ’Il‘y to be as neat
as possible. No books, calculators or notes allowed. In all the problems, the independent variable is x or t and the dependent variable is
y. Unless a method of solution is speciﬁed, you can use any correct method. Extra credit
Will be given by solving a problem by diHerent methods (if both solutions are correct). A general solution in the form F(a;,y) = C is acceptable when solving the equation
for y is too complicated. Score Problem 1
Problem 2 Problem 3 Problem 4 Problem 1 (20 points) A mass of 100K 97“. stretches a spring 5m when you hang the mass from the spring. Suppose that the mass is also attached to a damper of constant
400Newt0n — sec/ cm. If the mass is pulled 20m and then released without initial velocity,
ﬁnd its position as a function of time. (Use the acceleration of gravity 10m/sec‘2.) M mg m a mum) trig/1W M05 mama 7a WW 055m mm % W=10612362.8%2:730N
T/MW Matt/{lily b:— 7QON/6/mz/‘7é N/%
m M/p k) W (A6 {/9 WMQCZWVLQ) (12)de «65¢?sz :0
L/
MOVEEVE Problem 2 (20 points) 1) Use the method of undetermined coefﬁcients to ﬁnd a
particular solution of the equation 31(4) — 231(2) + y = 2et 2) Write the general solution of the equation in part 1) Problem 3 (20 points) Use the method of variation of parameters to ﬁnd the general
solution of the equation tgy” — 231 = 2t3 knowing that 3/1 (t) = t2, y2(t) = t‘1 are solutions of the homogeneous equation.
We not a t t mme WWW
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a W“? %’ 214 @7275
f/LQ WW/y/LW 0%? (gt )%2 W
l 762 7t
W: 276 76’2 1% we Maxim AjF: M,(t)(é,(%)+bézd') 92%) 5" Problem 4 (20 points)
Solve the initial value problem y" —— 21/ +43; 2 0; y(0) = 1;y’(0) =1 using Laplace transform. Partial credit will be assigned by solving the the problem by any other method. Also,
extra credit will be assigned by solving it by Laplace’s method and another method. $3
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 Fall '08
 Fonken
 Differential Equations, Equations

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