00:01
In this question we have to find laplace transform of the following functions.
00:10
The first function given to us in the question is 5 -e raised to the power 2t -t square so this implies you have to find laplace transform of 5 - laplace transform of e raised to the power 2t - laplace transform of t square so this implies you have laplace transform of 5 will be equals to 5 times laplace transform of 1 which is equals to 1 by s.
00:41
So we have 1 by s multiplied by 5 which is equals to 5 by s.
00:47
Similarly laplace transform of e raised to the power at is equals to 1 upon s minus a.
00:55
This is equals to 1 upon s minus 2.
00:58
The laplace transform of t raised to the power n is equals to n factorial upon s raised to the power n plus 1.
01:07
So the final answer to the first part of question is 5 upon s minus 1 upon s minus 2 minus 2 upon s cube.
01:16
So this is the final answer to the first part of the question.
01:20
Now we have the second part of the question.
01:22
So in the second part you find laplace transform of t cube e raised to the power 5t minus t.
01:30
It is minus e raised to the power t cos under root 7t.
01:39
So this implies we have to find the laplace transform of t cube e raised to the power 5t minus laplace transform of e raised to the power t cos under root 7.
01:55
So this implies laplace transform of t raised to the power n multiplied by e raised to the power at is equals to n factorial upon s minus a raised to the power n plus 1.
02:14
This implies we have laplace transform of t cube multiplied by e raised to the power 5t is equals to 6 upon s minus 5 raised to the power 4.
02:28
Similarly we have laplace transform of e raised to the power at multiplied by cos of kt is equals to s minus a upon s minus a whole square plus k square.
02:42
So this implies laplace transform of e raised to the power t cos under root 7t is equals to s minus 1 upon s minus 1 whole square plus 7...