Question: 3. Solve the following differential equations [analytically by using Laplace transform] dx a) +16 + 3x = 5cos3t where x(0) = 0, dx(0) dt

3. Solve the following ditferential equations analytically by using Laplace transform] d2x dt2 d2x +163x 5cos3t where x(0)=0, =0 dt where x(0) = 0, ?@ = 0 dt CHECK YOUR ANSWER BY MATLAB 4. By using MATLAB find poles and zeros for the following transfer function. Then find inverse Laplace. 100 (s 5)(s 70) s(s+45) (s 55)(s2 7s 110)(s2 + 6s + 95) G(s)

3. Solve the following differential equations [analytically by using Laplace transform] dx a) +16 + 3x = 5cos3t where x(0) = 0, dx(0) dt dt dx b) dx (0) + + 3x = 5e-t + t where x (0) = 0, = 0 dt dt dt CHECK YOUR ANSWER BY MATLAB 4. By using MATLAB find poles and zeros for the following transfer function. Then find inverse Laplace. 100(s+5)(s +70) G(s) s(s+45) (s +55) (s +7s + 110) (s + 6s +95)

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