Compute the Laplace transform L(f)(s) of the following...

Transcript

00:01 In this problem we have to find the laplace transform of the function first one is here we have three problems so first problem is f t equal t cube plus 2 t square e to power t so taking laplace laplace la place la place of f t is equal laplace of t q plus 2 t square e to power t since the laplace transform is a linear operator so using this property laplace of t t cube plus 2 la place of t squared e to power t so we will use here a formula la place of t power n is equal n factorial by s power n plus 1 and also la place of t power n f t is equal minus minus 1 power n minus 1 power n d power n by d s power n f s f s is the laplace transform of f t so using this we have 3 factorial by s power 3 plus 1 and plus 2 and here n equal to so we have minus 1 power n so minus 1 square d square by d s square and laplace of e to power t is 1 by s minus 1 so this is equal to 6 by s power 4 plus 2 and d by d s and the differentiation of 1 by s minus 1 is minus 1 by s minus 1 whole square.

01:46 So 6 by s power 4 plus 2 and derivative of minus 1 by s minus 1 whole square is minus 1 and minus 2.

01:58 So 2 by s minus 1 whole cube so this is equal to laplace of f s equal 6 by s power 4 plus 4 by s minus 1 cube so this is the laplace transform of the first function now the problem 2 is here f t equal sine 2 t so laplace transform of f t equal la plus of sine 2 t so the formula for la plus a t equal a by s square plus a square so a is here 2 so we have 2 by s square plus 2 square so la plus of f s so la plus of f s equal 2 is 2 by s square plus 4 this is the laplace transform of the function 2 now we will find the laplace transform for the given function f t equal e to power 3 t cos 2 t so taking the laplace transform we have la plus ft equal la place of e to power 3 t cos 2 t so using the formula la place of e cos bt.

03:49 So e to power a t cost b t is s minus a by s minus a whole square plus b square...

Question

Compute the Laplace transform L(f)(s) of the following functions: 1. f(t) = t^3 + 2t^2e^t 2. f(t) = sin(2t) 3. f(t) = e^{3t} cos(2t)

Question

Compute the Laplace transform L(f)(s) of the following functions: 1. f(t) = t^3 + 2t^2e^t 2. f(t) = sin(2t) 3. f(t) = e^{3t} cos(2t)

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