Question

1. determine the Laplace transforms of the following convolution integrals. hint: your solution will look like...

1. determine the Laplace transforms of the following convolution integrals.
hint: your solution will look like H(s) = F (s) × G(s) you are not solving an equation, merely translating the functions in t to their respective functions in s.

a. h(t) = (integral from 0 to t) (t - tau)^2 × cos(2×tau) dtau

b. h(t) = (integral from 0 to t) e^-(t - tau) × sin(tau) dtau

c. h(t) = (integral from 0 to t) sin(t-tau) × cos(tau) dtau

2. determine the inverse Laplace transform of the functions.
hint: simply right the convolution integral, do not evaluate it.

a. F(s) = 1 / (s^4 • (s^2 + 1))

b. F(s) = (2•e^(-2s)) / (s^2 - 4)

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