With the help of fourier transform obtain the convolution

Question

1. With the help of Fourier transform, obtain the convolution

y(t) = x(t) * h(t)

Given:

x(t) = δ(t) - e^-t u(t)

h(t) = e^-2t u(t)

2. If the frequency response of a system is given as

H(j?) = ((jw))/((1+(jw) )(2+(jw)))

Obtain the time domain relationship between y(t) and x(t)

3. Determine the Laplace Transform of the following:

a. 2e^-t+ t

b. 2Sin3t + cos3t

c. 4e^2t + 3 cos 4t

4. What is the inverse Laplace transform of:

((s² - 15s + 41))/((s+2) (s-3)²)

5. What is the inverse Fourier Transform of the following:

5/(6 + 5jw - w²)