Given the following functions F(s), find f(t). Note: Derive an expression in terms of cosine with a phase angle as discussed in the text, rather than using both cosine and sine functions. The form with a single trigonometric function is much more useful in practice as it shows the phase behavior more clearly.

Given the following functions F(s), find f(t). Note: Derive an expression in terms of cosine with a phase angle as discussed in the text, rather than using both cosine and sine functions. The form with a single trigonometric function is much more useful in practice as it shows the phase behavior more clearly.

(a) F(s) = 10/(s^2 + 2s + 2)

(b) F(s) = 8(s + 1) /(s^2 + 4s + 5)

(a) Find f(t) at t = 1. (b) Find f(t) at t = 1.

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