Final Homework - t =[t1,t2,t3,t4 total time interval x...

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Christopher Belcastro I.D. - 904424264 ECE 2704 – Homework #2 20 September 2006 Problem 5.3.3 (a)(vi): Problem 5.3.5 (a,b): a) 2 1 t + 2 1 [u s (t+1) - u s (t)] ( I ) - 2 1 [u s (t-1) - u s (t-1.5)] ( II ) e (-5t+7.5) [u s (t-1.5) - u s (t-2.5)] ( III ) b) Matlab Code: clear dt = 0.05; % time increment for plotting t1 = [-1:dt:0]; % first interval x1 = .5.*t1+.5; % signal on first interval t2 = [0:dt:1]; % second interval x2 = 1.*(t2/t2); % signal on second interval t3 = [1:dt:1.5]; % third interval x3 = -(1/2).*(t3/t3); % signal on third interval t4 = [1.5:dt:2.5]; % fourth interval x4 = exp(-5*t4+7.5); % signal on fourth interval
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Unformatted text preview: t = [t1,t2,t3,t4]; % total time interval x = [x1,x2,x3,x4]; % total signal plot(t,x) Problem 3.2.1 (a,b,c)(ii): a) (s – 3) 2 + 25 = (s – 3) (s – 3) + 25 = s 2 – 6s + 9 + 25 Therefore, standard second-order form is: s 2 – 6s + 34 ω n 2 = 34 Therefore: ω n = 34 = 5.83 Then it follows that 2ζω n = -6 Therefore: ζ = 34 2 6-= - 0.5144 b) Vector and Command: P = [1 -6 34]; damp(P); Damping (ζ) = -5.14e-001 Freq. (rad/s, ω n ) = 5.83e+000 Eigenvalue = 3.00e+000 + 5.00e+000i & 3.00e+000 - 5.00e+000i c)...
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