Determine the Laplace transform of the following...

Determine the Laplace transform of the following function: f(t) = 3 + 7t + t^2 + ?(t) Find the time domain function for the following Laplace transforms: a) F(s) = (s + 4) / (s + 5) b) F(s) = 7 / (s(s + 3))

Transcript

00:01 In this question, we have to determine the laplace transformation of the function which is given to be ft equal to 3 plus 70 plus t squared plus sigma.

00:16 Now we have to determine the laplace transformation.

00:19 Now, first of all, note that l of any function ft is going to be, laplace transformation is going to be 0 to infinity, a raised to the power minus ft, t raised to the power minus ft, t raised to the power.

00:32 N minus 1 d t which is going to be gamma n divided by s raised to the power n which is equivalent to n minus 1 factorial s raised to the power n using this we are given this function so l of function f t is going to be three times of 0 to infinity e raised to the power minus st d t plus seven times of 0 to infinity t multiplied by a minus st d t plus 0 to infinity e raised to the power minus s t t squared d t plus 0 to infinity e raise to the power minus s t s t sigma t d t so solving this we will have 3 divided by s plus 7 divided by s square plus 2 divided by s q plus 1 so this is going to be a final answer now we have to find out we have to find out the time domain function for the given laplace transformations.

01:38 So the first laplace transformation which is given is f s equal to s plus 4 divided by s plus 5.

01:47 Now we have to find out laplace transformation for this.

01:50 This can be written as 1 minus 1 divided by s plus 5.

01:54 Okay.

01:55 Now f t is going to be l inverse of this function f s which is going to be l inverse of 1 minus l inverse of 1 minus l inverse of 1 divided by s plus 5, which is going to be sigma t minus e raised to the power minus 5 t...

Question

Determine the Laplace transform of the following function: f(t) = 3 + 7t + t^2 + ?(t) Find the time domain function for the following Laplace transforms: a) F(s) = (s + 4) / (s + 5) b) F(s) = 7 / (s(s + 3))

Please give Ace some feedback