Question 1 From the shown system response to a 5 volts step find:

a) The % of overshoot

b) The damping ratio

c) The peak time

d) the settling time

e) The transfer function

Question 2. Consider the pole-zero plot of the transfer function H(s) given in Figure.

(a) If the dc gain is 2, find H(s).

(b) Compute the impulse response. Identify the steady-state and transient parts of the response.

(c) Compute the step response. Identify the steady-state and transient parts of the response.

CHECK. Your answer to (b) should be the derivative of your answer to (c), since the delta function is the derivative of the step function.
(d) If the input is 10e^-atu(t), find the pos-itive number a such that the response does not have a term of the form Ke^-atu(t).

Find the zero-state response under this condition. Identify the transient and steady-state responses.

Question 3. Simplify the following block diagram using the block diagram simplification rules and find out the overall transfer function G(s) = C(s)/R(s)

Caution: Just becaust a block has a 'H' in it, don't assume it is on the feedback path.

b) Convert the above graph into a signal flow graph. and clod the transfer function using Mason's gain formula to verify that the result tallies with that in 2 (a).