Question

Find the (zero-state) response for inputs x1(t) = 10u(t) and x2(t) = u(t −5).

A) Convolution Integral
B) Laplace Transform
C) Fourier Series
D) Green's Function

Answer 1

The (zero-state) response for the given inputs can be found using the convolution integral.

Step-by-step explanation:

The (zero-state) response can be found using the convolution integral.

1. Given x1(t) = 10u(t), we can find its Laplace transform as X1(s) = 10/s.
2. Similarly, x2(t) = u(t-5) can be transformed as X2(s) = e^(-5s)/s.
3. Multiplying X1(s) and X2(s), we get the Laplace transform of the response Y(s) = 10e^(-5s)/s^2.
4. Finally, taking the inverse Laplace transform of Y(s), we get the zero-state response y(t) = 10tu(t-5).