Chapter 5.8, Problem 22P

Unit Step Responses. The unit step response of a system is the output $y\left(t\right)$ when the input is the unit step function $u\left(t\right)$ and all initial conditions are zero.

(a) Show that the derivative of the unit step response is the impulse response.

(b) Plot and graph on the same set of coordinates the unit step response of

$y\text{'}\text{'}+2\delta y\text{'}+y=u\left(t\right)$

for $\delta =0.2,0.3,0.4,0.5,0.6,0.8,$ and $1$.