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### hw7-solns

Course: ASE 330M 18510, Spring 2011
School: University of Texas
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University of Texas - ASE 330M - 18510
University of Texas - ASE 330M - 18510
University of Texas - ASE 330M - 18510
ASE 330M Linear System AnalysisUnique Number: 12495, Spring 2006Revised Homework #1Math ReviewComplex Numbers and Ordinary Dierential EquationsDate given: January 24, 2006Date Due: February 2, 20061. Convert the following complex numbers to polar c
University of Texas - ASE 330M - 18510
ASE 330M Linear System AnalysisUnique Number: 12495, Spring 2006Revised Homework #1Math ReviewComplex Numbers and Ordinary Dierential EquationsDate given: January 24, 2006Date Due: February 2, 20061. Convert the following complex numbers to polar c
University of Texas - ASE 330M - 18510
2/16/06 12:24 PM\ase-lrc-server\home\rdc55\Desktop\Linear\systems_2hw.mt=[-5:.01:5]d=[-2*pi:(4*pi/1000):2*pi]t1=t[y1]=fx(t1)figure (1)y1=sin(y1)plot (d,y1)t2=2*t[y2]=fx(t2)figure (2)plot (t,y2)t3=t[y3]=fx(t3)figure (3)plot (t,y3)t4=2*t[y
University of Texas - ASE 330M - 18510
University of Texas - ASE 330M - 18510
University of Texas - ASE 330M - 18510
University of Texas - ASE 330M - 18510
University of Texas - ASE 330M - 18510
ASE330MHomework#6DueNovember16th,2007.Problem#1Consideramassonaflatnonsmoothsurface,subjecttoaforce F ( t ) .Thesurfacefrictionisdirectlyproportionaltothevelocityoftheparticle, x ,throughafrictioncoefficient .Thus,theequationofmotionfortheparticlecan
University of Texas - ASE 330M - 18510
ASE330MHomework#6DueNovember16th,2007.Problem#1Consideramassonaflatnonsmoothsurface,subjecttoaforce F ( t ) .Thesurfacefrictionisdirectlyproportionaltothevelocityoftheparticle, x ,throughafrictioncoefficient .Thus,theequationofmotionfortheparticlecan
University of Texas - ASE 330M - 18510
ASE330MHomework#3Problem#1:Findtheequilibriumsolutions,iftheyexist,foreachofthefollowingsystems:(a)x1 = x2x2 = x1 + 1(b)(c)x1 = x2x2 = 1x1 = x2x2 = x1 x13(d)x1 = x2x2 = 0Problem#2:Obtainallequlilibriumsolutionsforthefollowingsystem:( cos
University of Texas - ASE 330M - 18510
ASE330MHomework#3Problem#1:Findtheequilibriumsolutions,iftheyexist,foreachofthefollowingsystems:(a)x1 = x2x2 = x1 + 1(b)(c)x1 = x2x2 = 1x1 = x2x2 = x1 x13(d)x1 = x2x2 = 0Problem#2:Obtainallequlilibriumsolutionsforthefollowingsystem:( cos
University of Texas - ASE 330M - 18510
University of Texas - ASE 330M - 18510
ASE 330MProblem Set 71. Use Matlab to plot the following functions for 1 t 5 .a. x ( t ) = 3e2t 1( t )b. x ( t ) = e2t ( sin 3t )1( t )c.x ( t ) = e j 3t 1( t ) 1( t 3) 2. Sketch, by hand, the following signalsa. x ( t ) = 1( t + 1) 2 1( t 1) + 1(
University of Texas - ASE 330M - 18510
University of Texas - ASE 330M - 18510
ASE330MHomework#7(ForExtraCreditOnly)Due:December7th,2007Problem#1:UsethemethodofpartialfractionexpansiontoidentifytheinverseLaplacetransformofthefollowingfunctions:(a) F ( s ) =1s ( s + 1)(b) F ( s ) =10e 3 s ( s + 2 )( s + 10 )(c) F ( s ) =(
University of Texas - ASE 330M - 18510
University of Texas - ASE 330M - 18510
% Homework 5, Problem 1clear allclose allclc% Problem 1a.) Plot x(t) = 3exp(-2*t)*1(t)t = (-1:0.01:5);jj_minus = find(t&lt;0);jj_plus = find(t&gt;=0);one = zeros(size(t);one(jj_plus) = ones(size(t(jj_plus);x = 3*exp(-2*t).*one;subplot(3,1,1)plot(t,x
University of Texas - ASE 330M - 18510
ASE 330M Linear System AnalysisUnique Number: 12880, Spring 2007Revised Homework #1Review on Complex Number VariablesDate given: January 25, 2007Date Due: February 1, 20071. Convert the following complex numbers to polar coordinate (exponential) for
University of Texas - ASE 330M - 18510
University of Texas - ASE 330M - 18510
ASE 330M Linear System AnalysisUnique Number: 12880, Spring 2007Homework #2Math ReviewOrdinary Dierential Equations &amp; Matlab ExercisesDate given: February 6, 2007Date Due: February 15, 20071. State whether the following ordinary dierential equation
University of Texas - ASE 330M - 18510
% Problem B14w1=exp(j*pi/2)*ones(3,1)-[2*exp(j*pi/6);2*exp(3*j*pi/2);2*exp(17*j*pi/6)];% Problem B.22 (a)t1 = [0:0.01:10]';x1 = real(2*exp(-1+2*pi*j)*t1);% Problem B.22 (b)x2 = imag(3*ones(length(t1),1) - exp(1-2*pi*j)*t1);% Problem B.22 (c)x3 = 3
University of Texas - ASE 330M - 18510
University of Texas - ASE 330M - 18510
ASE 330M Linear System AnalysisUnique Number: 12880, Spring 2007Homework #3Basics of Signals and SystemsDate given: February 22, 2007Date Due: March 6, 20071. The systems given below have input x(t) and output y (t) respectively. Determinewhether e
University of Texas - ASE 330M - 18510
ASE 330M Linear System AnalysisUnique Number: 12880, Spring 2007Homework #4Impulse and Step Response for LTI SystemsDate given: March 1, 2007Date Due: March 20, 20071. An LTI system has an impulse response h(t) = (et + sin t)u(t).(a) Evaluate the s
University of Texas - ASE 330M - 18510
ASE330MHomework4Lasttime(springmassdamper):4,5eigenvaluesatcosForsin0015Therefore,,5where, 15,,152ForHomework:(1) ForthesameproblemdiscussedaboveFindfor2;a)b) sinc);givenby01;003;01;1;00(2) Verifythesolutionsint
University of Texas - ASE 330M - 18510
University of Texas - ASE 330M - 18510
ASE 330M Linear System AnalysisUnique Number: 12880, Spring 2007Homework #5Frequency Response FunctionBIBO StabilityDate given: March 29, 2007Date Due: April 10, 20071. An LTI system has a step response (et sin t)u(t).(a) Determine whether the sys
University of Texas - ASE 330M - 18510
% Homework 5, Problem 1clear allclose allclc% Problem 1a.) Plot x(t) = 3exp(-2*t)*1(t)t = (-1:0.01:5);jj_minus = find(t&lt;0);jj_plus = find(t&gt;=0);one = zeros(size(t);one(jj_plus) = ones(size(t(jj_plus);x = 3*exp(-2*t).*one;subplot(3,1,1)plot(t,x
University of Texas - ASE 330M - 18510
University of Texas - ASE 330M - 18510
ASE 330M Linear System AnalysisUnique Number: 12880, Spring 2007Homework #6Date Given: Wednesday, April 11, 2007Due Date: Monday, April 23, 2007For this homework, when necessary, you are permitted use of MATLAB and/or calculator inevaluating roots o
University of Texas - ASE 330M - 18510
University of Texas - ASE 330M - 18510
ASE 330M Linear System AnalysisUnique Number: 12880, Spring 2007Homework #7Date Given: April 24, 2007Due Date: May 1, 2007For this homework, unless otherwise indicated, you are permitted use of MATLAB and/or calculatorin evaluating roots of polynomi
University of Texas - ASE 330M - 18510
University of Texas - ASE 330M - 18510
ASE 330M Linear System AnalysisUnique Number: 12880, Spring 2007Homework #8Date Given: May 1, 2007Due Date: May 9, 2007 at 10.00am1. An LTI system at zero initial conditions is subject to an input signal x(t) = te3t u(t). Theresulting output is desi
University of Texas - ASE 330M - 18510
University of Texas - ASE 330M - 18510
ASE 330M Linear Systems: Fall 2008Homework #3: Due 10/7/2008 by 5PMConsider the linear systems described by the differential equations below:a)D2 5 D 6 y t D 1 u t u t 6y 0 2, y 0 1b)D2 4 D 4 y t Du t u t sin 3ty 0 3, y 0 4c)D D 1 y t D 2
University of Texas - ASE 330M - 18510
ASE330MHomework#4Problem#1:1.22(Textbook)Problem#2:Consideradifferentialequationin y t characterizedbydifferentialoperatorsQ D D 2 D 3 ,P D 1.Supposethesystemisinitiallyatrest( y 0 0 , y 0 0 ).Findthecompletesolutioniftheforcinginputsignalisgiven x
University of Texas - ASE 330M - 18510
ASE330MHomework#6DueDecember5th,2008ReadingAssignment:Sections4.5,4.7,and4.8Problem#1,Fortheunityfeedbacksystembelow,identifythefollowingquantities:(a)Theplanttransferfunction, Y s / U s (b)Thecontrollertransferfunction, U s / E s (c)Theclosedloopt
University of Texas - ASE 330M - 18510
ASE 330M Homework #1 (Review of Vectors &amp; Dynamics)Due: Friday, September 14th.Reading Assignment: Read Chapters 1-3 of Torby (available as PDF from blackboard)Problem #1:During the encounter with the asteroid Gaspra, the Galileo spacecrafts position
University of Texas - ASE 330M - 18510
University of Texas - ASE 330M - 18510
University of Texas - ASE 330M - 18510
University of Texas - ASE 330M - 18510
University of Texas - ASE 330M - 18510
University of Texas - ASE 330M - 18510
ASE330MFall2008:Homework#2DueMonday,September29thThe diagram below illustrates a particle P of mass m that is constrained to move radially along arecessed channel on a spinning turntable. The motion of the mass is subject to some stiffness andfriction
University of Texas - ASE 330M - 18510
University of Texas - ASE 330M - 18510
University of Texas - ASE 330M - 18510
University of Texas - ASE 330M - 18510
University of Texas - ASE 330M - 18510
University of Texas - ASE 330M - 18510
(i) M.(l4tuMA.~(A.lA,tock( =~~!: 0 ~ l) h'~.L7 s1a.,\e as tAo.~.0.)N.J- e,d~(&quot;:fottt'\$*-nMe. \)Wl~' s J.tJ lAwrr ., -_&quot;'t'I\. Tot~ ,~-aJ'TNt' -':)0# .b E=v.\~r ~ \.,a.v.,')-0M=~*' .,.f(._c~tf01 ~W ~U.~e&quot;_ ~ dt.u-a 1\ \4~ .MOIt\Qt\
University of Texas - ASE 330M - 18510
RSE '53oJJ., - I.tc.~-=t 2 .12-0 b I N' .&gt; 0HI:)fi-4' .fULS~\ &lt; lI-rI&quot;.I - z. ~oI &quot; '-W~W i.cfw_12A Ib-tt-.vt1.0+t'\'\.ll\.e (N0. tYse~.~. tvcw.- - -~-~.- .o.,'~e. ~ _ oV(); \13--d-lvd _o~Iecit0.e. d-P&gt;PwJb-.,J-~b Y
University of Texas - ASE 330M - 18510
~\i\ ~ ca M~\s ~ 0 oh. A.r, e=:5(tF BD: l+- e~&quot;bl' - v'-~e -op'PA13r~&quot; 'e3&quot;'-tl-0H--0M =~'D-0M. a&quot;'AA:-=-)v\b~-~-~-\JX:it 13-t A\'L b&quot;z +.&quot;' +~f\b~ + ~1-b~--~-~-At=JJ\'J,00twJ,z'e :~-.t\-lfoM.\1&amp;-2~-f/
University of Texas - ASE 330M - 18510
-LA01cfw_\ ~Cc:~l)c/c.l.A1- 00D0:=.bii&quot;,1tz,US! 1tu&quot;A.lIJA-xISlkoWv--=To0,;:c:= C./ 0Thl'2--.B,,, C&gt; IIl:)tJ~0olC&gt;D\&quot;3~'2M0=--_0+tIe.~cw-C/oetC;e~cw00eo- 0_0t\-2.1 n ,3t\~ee-1)H-,
University of Texas - ASE 330M - 18510
l et-iu~ e- =tt= lR.9/ tol~oJLoAQ.(2i(~ [N+eJ'(a-h'~ = 7 A-PPR-at(.of- ~ '1Jw-llv\&amp;rl&quot; oldN/vv\l(! bdw~. t -.- -l ~ tLll\.tho.R &quot;I\cfw_)J(\J~ ~.Ie i. ~ t\M-tt f ex):=; ; = .;.~te I/t'Ll-ov- ~ ilt;)f~L- ~.of- 1:Xlt~ : I lUIW cY cDNd. i~' ~-=
University of Texas - ASE 330M - 18510
e.&quot;':'-OPrI .L:=C~)&lt;&quot;f:e.-oP~ Y-(re~-\-'S ~)~ t- lre +.~ So')l-~1e,.\- t(~40So -\- lv-B ~)4 1~z.: [-re'2.~- 5~&quot;-Y~- (&quot;e5E&gt;1~.&amp;&lt;.~oP'&lt;e =\-(&quot;.;Ce +-'~V~t\ -Y9~ - ~ - r9 Se.l ~+L-r9&quot;'~&amp;+recel~'Z-fl. 4. F.&gt;Ot.\~( j):~ C~.l&quot;~i.~1: ~s:e.
University of Texas - ASE 330M - 18510
LeJ:J-(.q o\4a-fe -fk\ V'\~Je.stj~Cl)&quot;) -=~~' tilbJM\;~ ~-Lv o.j.i'kb\e~Cl-t-@0+- ~j +~ ~ f~) =- /A it ,70 ~o)\llol.okfcfw_etlM-h'4 &quot;fer2o.:M&lt;.~~l1?~lt)~ 'tC0~UL+)Qcfw_t-'(S-C1)-=-D t~1)2-:1)~1) + ~. 1dt.~dtz( 1)'L +- ~1) + 7'M
University of Texas - ASE 330M - 18510
5 1\-'[,- l()-:- -~-:_b_uJ_ee~_lotel\~'~ .:! e i : Cos ()f i SiN eI e- 11\ 0fti~i=f-J-~-~-~-~-~-~-~-~-~ ~-\.-~-~&quot;Jr :=-A- : 1 CAs ~ -I L ~itJ 9:- Cd):; = -SiN'G- -I:- C Co s 9dEt-' = [ [tS '~i~&amp; + cose:]- -A14k.:- ct~-~ ~\ f)it.ed&amp;
University of Texas - ASE 330M - 18510
Le cAu e =#' n: 9J-l \ O'gCQ Cl)')~l-h)1 (t)~ ~ l-t-Lr = T&gt;Ll)tt(+)+ &quot;j- LtJ~~-~:f:(20- oS~-le.mputt~p&quot;,a:tTlU (c.,L7f-fA'-'V,. ~l'.OV ~ 'rW'I\I\C.AU ,-Las+ 1(Me;VcQ C~) = 0 ~?~~o It):= ~ C~- C:x. '.(J):J b ([AtIi.K:. (