1. (25 p). Use the Laplace transform to compute the solution of the differential equation y"(t) + 3y'(t) = x(t)- y(t), x

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1 25 P Use The Laplace Transform To Compute The Solution Of The Differential Equation Y T 3y T X T Y T X 1 (49.46 KiB) Viewed 14 times

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1. (25 p). Use the Laplace transform to compute the solution of the differential equation y"(t) + 3y'(t) = x(t)- y(t), x(t) = u(t), y(0) = 2, y'(0) = 1. Plot the solution in the time interval 0 st < 10. 2. (25 p). Use the Laplace transform to find the solution of the differential equation y"(t) + 4(t) + 3y(t) = x(t), y(0) = 2, y'(0) = 2. The signal X(t) is given by: 1, t<3 x(t) = {t-3, 3 st<6. 3, t> 6 3. (25 p). Use the Laplace transform to find the solution of the differential equation y"(t) + y'(t) – 2y(t) = 8(t), y(0) = 4, y'(0) = 2, y"0) = 3. 4. (25 p). Consider a different system function, 4 H(s) = $2 + s + 16.25 Re(s) >- 2 Find and plot the poles of this system function using pzplot function of MATLAB