00:01
In this question we need to find out what is the inverse laplace transform of the following function.
00:06
The function is f of s is equals to 3 times s plus 1 over s square plus 1.
00:15
Okay, so here our aim is to find out what is the inverse laplace transform of the given function.
00:28
Let us see how we are going to do this.
00:32
So, l inverse of f of s will be nothing but l inverse of 3s plus 1 over s square plus 2.
00:43
So, this is the inverse laplace operator l inverse.
00:48
Okay, so this can also be written as l inverse 3s over s square plus 1 plus 1 over s square plus 1.
01:02
We have just split it or separated the numerator.
01:06
Okay, so this is what we get.
01:09
Now, we will use the linearity property.
01:13
So, linearity property let me first write down here.
01:18
So, it is given by l inverse of let's say we have two function a times f of s plus b times g of s.
01:32
So, linearity says this is same as a times l inverse of f of s plus b times l inverse of g of s.
01:45
So, we can use this property over here...