00:02
Hello students, in the first part, eighth question is we need to find the laplas transform of f of t equals 3e power minus 5 t plus 6e power minus 3t.
00:14
We know that the formula l of e power minus 80 is 1 by s plus a.
00:22
So on taking laplas transform, then we get f of s equals 3 by s plus 5.
00:30
Plus 6 divided by s plus 3.
00:36
Therefore on taking lcm we get f of s equals 9 s plus 39 divided by s plus 5 into s plus 3.
00:50
In the beat question given function f of t equals cos 3 t plus 3e power minus 2 t, sine 5 t.
01:03
We know that the formula of l of cos a t equals s divided by s squared plus a square and l of sine a t equals a divided by s square plus a square and l of e power a t, f of f of s minus a.
01:32
Therefore, on applying the laplace transform we get f of s equals.
01:38
By using the first formula we can write it as s divided by s squared plus 3 squared that is 9.
01:45
By using the second and third formula we can write it as 3 into 5 divided by s squared plus 25.
01:57
Here s equals s plus 2 because yes.
02:04
A is minus 2 minus into minus plus 2.
02:09
Therefore, we conclude that the final answer f of s equals s divided by s squared plus 9 plus on substituting s for s plus 2, then we get 15 divided by s plus 2 the whole square plus 25...