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### hw5

Course: ASE 330M 18510, Spring 2011
School: University of Texas
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330M ASE Linear System Analysis Unique Number: 12495, Spring 2006 Homework #5 Date Given: March 28, 2006 Due Date: April 6, 2006 For this homework, you are permitted use of MATLAB and/or calculator in evaluating roots of polynomials order higher than 2. 1. Determine the unilateral Laplace transform of the following signals: (a) x(t) = et (t 2)u(t 2) (b) x(t) = et u(t) cos(t 2)u(t 2) 2. Consider a signal x(t)...

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330M ASE Linear System Analysis Unique Number: 12495, Spring 2006 Homework #5 Date Given: March 28, 2006 Due Date: April 6, 2006 For this homework, you are permitted use of MATLAB and/or calculator in evaluating roots of polynomials order higher than 2. 1. Determine the unilateral Laplace transform of the following signals: (a) x(t) = et (t 2)u(t 2) (b) x(t) = et u(t) cos(t 2)u(t 2) 2. Consider a signal x(t) satisfying x(t) = 0 for all t < 0. Determine the signal initial value x(0+ ) and nal value x() if the unilateral Laplace transform X (s) is given by: (a) X (s) = 2e5s /[s(s + 2)] (b) X (s) = (2s + 3)/(s2 + 5s + 6) 3. Find the inverse Laplace transform of the following functions: (a) X (s) = s/(s4 + 2s + 3) (b) X (s) = (s2 + s 3)/(s2 + 5s + 6) (c) X (s) = (4s2 6)/(s3 + + s2 2) 4. The transfer function of an LTI causal system is given by H (s) = 4s2 + 8s + 10 2s3 + 8s2 + 18s + 20 Evaluate the step response of this system. 5. An LTI causal system with zero initial energy is subjected to an input signal x(t) = e3t cos(2t)u(t). The resulting output is given by y (t) = t3 e2t sin(t) u(t). Your tasks are as follows: (a) Find the transfer function. (b) Find the systems impulse response function. (c) Obtain the step response of the system. (d) Determine the output of this system for an input x(t) = sin(t)u(t) for any (realvalued) frequency . Again assume zero initial energy at the time of input application. 6. The step response of an LTI system is given by g (t) = t2 cos(t) u(t 1). Determine the transfer function for this system.
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University of Texas - ASE 330M - 18510
ASE 330M Linear System AnalysisUnique Number: 12495, Spring 2006Homework #5Date Given: March 28, 2006Due Date: April 6, 2006For this homework, you are permitted use of MATLAB and/or calculator in evaluating rootsof polynomials order higher than 2.1
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
ASE 330M Linear System AnalysisUnique Number: 12495, Spring 2006Homework #6Date Given: April 11, 2006Due Date: April 18, 2006For this homework, unless otherwise indicated, you are permitted use of MATLAB and/or calculatorin evaluating roots of polyn
University of Texas - ASE 330M - 18510
ASE 330M Linear System AnalysisUnique Number: 12495, Spring 2006Homework #6Date Given: April 11, 2006Due Date: April 18, 2006For this homework, unless otherwise indicated, you are permitted use of MATLAB and/or calculatorin evaluating roots of polyn
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 2006Homework #7Date given: April 27, 2006Date Due: May 4, 20061. An LTI system has a step response (et cos2 t)u(t). Determine an ordinary dierential equation representation for this system.
University of Texas - ASE 330M - 18510
ASE 330M Linear System AnalysisUnique Number: 12495, Spring 2006Homework #7Date given: April 27, 2006Date Due: May 4, 20061. An LTI system has a step response (et cos2 t)u(t). Determine an ordinary dierential equation representation for this system.
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
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