HW4solns

# HW4solns - xlabel(’Time(s)’ 14 ylabel(’V{out(t)’...

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Problem 1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0 2 4 6 8 10 12 14 16 18 20 Impulse Response Time (sec) Amplitude Impulse Response Inverse Laplace Result Figure 1: Problem 1a, Blue line shows the impulse response of H ( s ) = 300( s +20) s ( s 2 +40 s +300 and the Red X shows the result of taking the inverse Laplace transform 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0 2 4 6 8 10 12 14 16 18 20 Impulse Response Time (sec) Impulse Response Inverse Laplace Result Figure 2: Problem 1b, Blue line shows the impulse response of H ( s ) = 200 s ( s +40)( s 2 +4 s +8 and the Red X shows the result of taking the inverse Laplace transform 13

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Matlab code F1=tf([300 300*20],[1 40 300 0]); impulse(F1); hold on; t=0:.01:.7; plot(t,-15*exp(-10*t)-5*exp(-30*t)+20,’rx’) F2=tf([200 0],conv([1 40],[1 4 8])); figure; impulse(F2); hold on; t=0:.01:2.5; plot(t,-5.52.*exp(-40.*t)+2.*3.72.*exp(-2.*t).*cos(2.*t+.73),’rx’) Problem 3 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 -0.1 0 0.1 0.2 0.3 0.4 0.5 0.6 Time (s) V out (t) Response of RLC Circuit in Prob. 3 Figure 3: Step response for Problem 3 Matlab Code t=0:.01:5; plot(t,sqrt(3)/3.*exp(-t).*cos(sqrt(3)*t-pi/6),’-k’,’LineWidth’,2);

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Unformatted text preview: xlabel(’Time (s)’); 14 ylabel(’V_{out}(t)’); title(’Response of RLC Circuit in Prob. 3’); grid on; Problem 4 1 2 3 4 5 6 7 8 9 10-0.2 0.2 0.4 0.6 0.8 1 1.2 Time (s) V out (t) Response of RLC Circuit in Prob. 4 Figure 4: Step response for Problem 4 Matlab Code t=0:.01:5; plot(t,2/sqrt(2).*exp(-t).*cos(t-pi/4),’-k’,’LineWidth’,2); xlabel(’Time (s)’); ylabel(’V_{out}(t)’); title(’Response of RLC Circuit in Prob. 4’); grid on; 15 Problem 5 1 2 3 4 5 6 7 8 9 10 0.5 1 1.5 2 2.5 3 3.5 4 Time (s) V out (t) Step Response of RLC Circuit in Prob. 5 Figure 5: Step response for Problem 5 Matlab Code t=0:.01:10; plot(t,20.*t.*exp(-2.*t),’-k’,’LineWidth’,2); xlabel(’Time (s)’); ylabel(’V_{out}(t)’); title(’Step Response of RLC Circuit in Prob. 5’); grid on; 16...
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HW4solns - xlabel(’Time(s)’ 14 ylabel(’V{out(t)’...

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