The response of a first-order system is for t ‰¥ 0

and zero otherwise.

(a) Consider y(0) = 0 is the system linear? If y(0) ‰  0, is the system linear? Explain.

(b) If x(t) = 0, what is the response of the system called? If y(0) = 0 what is the response of the system to any input x(t) called?

(c) Let y(0) = 0, find the response due to δ(t). What is this response called?

(d) When y(0) = 0, and x(t) = u(t) call the corresponding output s(t). Find s(t) and calculate ds(t)/dt, what does this correspond to from the above results?

Transcribed Image Text:

e-l-t)x(t)dt| y(t) = y(0)e¬' + (1-1)-