Question

3. A system is described by the differential equation dy dt + 2y (t) = 3x (t). (a) Find the impulse response of this system. (b) Find the step response of this system. (c) Find the response to the signal x (t) = rect(t 3).

Answer 1

a

The impulse response is
`h(t) = 3e^(-2t)u(t)`

b

The step response of the system is =
`y(t)=(3)/(2) [1-e^(-2t)]u(t)`

c

The response signal is

Output =
`(3)/(2) [1-e^{-2(t-(1)/(2) )}]u(t-(1)/(2) ) -(3)/(2) [1-e^{-2(t-(3)/(2) )}]u(t-(3)/(2) )`

Explanation:

The explanation is shown on the first and second uploaded image