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Unformatted text preview: EE — 350 ,, ' Exam 1 ‘ 4 February 2002
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E, Test Form A 19m You have 2 hours to complete the exam. Calculators are [not allowed. This exam is closed book. You may use one 8.5 " x 11" note sheet. Solve each part of the problem in the space following the question. If you need more space, continue your solution on the reverse side labeling the page with the question number, for example, "Problem 1.2 Continued". NO credit will be given to solutions that do not meet \ this requirement. ‘  ~ 5. DO NOT REMOVE ANY PAGES FROM THIS EXAM. Loose papers will not be accepted
and a grade of ZERO will be assigned. ‘ 6. If you introduce a voltage or current in the analysis of a circuit, you must clearly label the
new variable in the circuit diagram and indicate the voltage polarity or current direction. If
you fail to clearly deﬁne the voltages and currents used in your analysis, you will receive
ZERO credit. , 75‘ “The quality of your analysis and evaluation is as important as your answers. Your reasoning must be precise and clear; your complete English sentences should convey what you are
doing. To receive credit, you must show your work. " PWP?‘ Problem 1 (25 points) 1.1 (15 points) Determine if the following system, with input f(t) and output y(t), is zero—state
linear, time invariant and causal. Y(t)=cos(t)f(t+1) W
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n V mgs’k hCLVQ. 1.2 (10 points) Express the following function in terms of the unit step function, u(t), and
polynomials in t. mberce pt 4;
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Pa 3, O o’H‘QrwnW 1C (19 = 59. H57 + ﬁle) Problem 2 (25 points) 2.1 (9 points) Determine if the signal f (t) = 3e'2’u (—t) is a power signal, energy signal or
neither. If the signal is a power or energy signal, ﬁnd the appropriate measure. Rt) 2.2 (7 points) A system is modeled by the linear ordinary differential equation dfdf)+20f<t>=f’%,,ii’+25y<t> i) Is the system asymptotically stable? Justify your answer.
ii) Determine the rise time of the system's step response.
iii) Determine the settling time of the system's step response. 1) .7 ga Foot # 't’Q, aka. faLLQ VI 54739 e DyanElvn Jwﬂs‘plej QC?“ r— 7s+ 23‘ so
’2\ <0) tho. amQ. ‘ 7h: 25‘, (Se/CW 2.1.1) Tﬂe mSvltS '1!» parts (Li) uni can) 082 ‘ 4; s 0):!)
gas; w—ttoﬂs jQuQ’Qa/ci 'er ~PVS£ 'ofooQV‘ $65 em whom, no _—. o , $2.ch m :1 #0,, this Sarnéem/ the ttfva. vet/[v.99 % fr qmﬂ, *5 WI“ achéV‘ ‘Pram those ytven aboVQa 2.3 (9 points) Write the Matlab code necessary to generate a plot of y (t) = e‘a' cos (2t)u (t) on
the interval 0 S t S 3. Include appropriate labels on the x and y axis. 13 = anSFaLQ. (o, 33', 5L : QXFbBazﬂdk CoSCZekD') #lab‘8‘ ( \ anplft/OQQ' I) Problem 3 (25 points) 3.1 (8 points) For the linear circuit shown, ﬁnd the ordinary differential equation relating the
input signal f(t) to the output signal y(t). Place your answer in standard form. 3.2 (5 points) Find the characteristic equation of the system and its root(s). 79E, c\\aro.cLerxs—Hg eat/03:10!) 75 R‘a—R'I— = O L’\="\+
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ordinary differential equation dﬁi’)+6y<r>=4f<r>. Given the initial condition y(0+) = 3, ﬁnd the total response using the classical solution method. Ch OeV‘cLGLQ Y‘ 543%.. Q agate {an O! n be (*5 foo‘t ‘. 6? (ﬁ\ : 7‘ + 6 = O :2) ﬂ’ = ' 6
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39f(t)= (D2 +6D+13)y(t). Let f (t) = 311 (t), y (0+ ) = 3 , and dig) = —9. Determine the zerostate response.
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39f(t)=(D2+6D+13)y(t). Let f(t)=3u(t), J’(0+)=3,and dig) = —9. Detennine the zeroinput response.
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