Consider the following circuit, where C = 1 [F] and R = 0.5 [2]. + ww...

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Consider the following circuit, where C = 1 [F] and R = 0.5 [2]. + ww R + C Vo Vi R (a) Derive the transfer function G(s) = v(s). (b) Assume that the initial charge in the capacitor is zero. Obtain the response of the system, when vi(t) = 1, t 0 (i.e., obtain the step response). (c) Use MATLAB to plot the step response and verify your answer in Part (a). (d) Compute the time constant T for this system. As discussed in class, the step response should remain within 2% of the final value for t 4T. Is that true for this system? If not, explain the reason. (e) Compute the exact time when the steady state is reached? That is, the time when the response reaches 98% of the final value and remains within 2% of the final value afterwards. Consider the following circuit, where C = 1 [F] and R = 0.5 [2]. + ww R + C Vo Vi R (a) Derive the transfer function G(s) = v(s). (b) Assume that the initial charge in the capacitor is zero. Obtain the response of the system, when vi(t) = 1, t 0 (i.e., obtain the step response). (c) Use MATLAB to plot the step response and verify your answer in Part (a). (d) Compute the time constant T for this system. As discussed in class, the step response should remain within 2% of the final value for t 4T. Is that true for this system? If not, explain the reason. (e) Compute the exact time when the steady state is reached? That is, the time when the response reaches 98% of the final value and remains within 2% of the final value afterwards.