(3) [10+12pts] Find (a) the Laplace transform of f(t) = [sin(t) U(t 5) + t...

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(3) [10+12pts] Find (a) the Laplace transform of f(t) = [sin(t) U(t – 5) + t cos² (2t)]. (Here U (t – 5) is the step function.) 1 (b) inverse Laplace transform of G(s): (s² + 4s + 5)(s² – 9) (3) [10+12pts] Find (a) the Laplace transform of f(t) = [sin(t) U(t – 5) + t cos² (2t)]. (Here U (t – 5) is the step function.) 1 (b) inverse Laplace transform of G(s): (s² + 4s + 5)(s² – 9)