Question

The unit impulse response of a system is given as c(t) = -4e^-t + 6e^-2t. The step response of the system for t ≥ 0 is equal to
1. 3e^-2t + 4e^-t + 1
2. -3e^-2t + 4e^-t + 1
3. -3e^-2t + 4e^-t – 1
4. 3e^-2t – 4e^-t + 1

Answer 1

Correct Answer - Option 3 : -3e^-2t + 4e^-t – 1

Given unit impulse response is c(t) = -4e^-t + 6e^-2t

Step response = Integral of unit impulse response

\( = \mathop \smallint \limits_0^t \left( { - 4{e^{ - t}} + 6{e^{ - 2t}}} \right)dt\)

\( = \left[ {4{e^{ - t}} - 3{e^{ - 2t}}} \right]_0^t\)

= -3e^-2t + 4e^-t – 1