Question

(a) The first-order system has the transfer function T(s)=\frac{A}{1+s T} Find the system output response in time domain when a unit ramp signal, r(t)=t, is applied to its input. (b) The transfer function of a second-order system is: T(s)=\frac{4}{s^{2}+4 s+4} Find the system output response in time domain when a unit ramp signal, r(t)=t, is applied to its input. \text { (Note: The inverse Laplace transform of } F(s)=\frac{1}{(s+a)^{2}} \text { is } f(t)=t \cdot e^{-a t} \text {.) }

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