LAPLACE TRANSFORMS OF ELEMENTARY FUNCTIONS 51. Find the Laplace transforms of each of the following functions. In each case specify the values of s for which the Laplace transform exists. (a) 2e^4t Ans. (a) 2/(s - 4), s > 4 (b) 3e^-2t (b) 3/(s + 2), s > -2 (c) 5t - 3 (c) (5 - 3s)/s^2, s > 0 (d) 2t^2 - e^-t (d) (4 + 4s - s^3)/s^3(s + 1), s > 0 (e) 3 cos 5t (e) 3s/(s^2 + 25), s > 0 (f) 10 sin 6t (f) 60/(s^2 + 36), s > 0 (g) 6 sin 2t - 5 cos 2t (g) (12 - 5s)/(s^2 + 4), s > 0 (h) (t^2 + 1)^2 (h) (s^4 + 4s^2 + 24)/s^3, s > 0 (i) (sin t - cos t)^2 (i) (s^2 - 2s + 4)/s(s^2 + 4), s > 0 (j) 3 cosh 5t - 4 sinh 5t (j) (3s - 20)/(s^2 - 25), s > 5
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(a) 2e4t: s=0, 1, 2, 3, 4, 5 Show more…
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