First and second order systems Consider the series connection of a voltage source, r(t), a resistor (resistance R) and a capacitor (capacitance C). Define the output, yt) as the voltage across the capacitor. (a) Find the differential equation relating (t) and y(t). (b) Find the frequency response, H(jw) (c) Find the impulse response, h(t) (d) Is the system best described as low-pass, high-pass, band-pass or band-stop? (e) It is possible for the step response of this to have an oscillatory behavior?
(f) What is the asymptotic value of the step response, s(t) for large t? (s(oo) (g) Determine the time, to, for which s(to) = s(o) (1-e-2)