Find the Laplace transformation of the following functions: f(t)=e^(2t)times(t^2-cos3t)

Nica2t

Nica2t

Answered question

2022-08-10

Find the Laplace transformation of the following functions:
f ( t ) = e 2 t × ( t 2 + cos 3 t )

Answer & Explanation

Erika Brady

Erika Brady

Beginner2022-08-11Added 19 answers

Step 1
Given function;
f ( t ) = e 2 t × ( t 2 + cos 3 t )
Step 2
Given f ( t ) = e 2 t × ( t 2 + cos 3 t )
f = e 2 t + e 2 t cos 3 t ... 1
i.n.s e.n.s
Taking i.n.s f × H × S ; f e 2 t t 2 = ( 11 2 × 2 ! ( 5 2 ) 3 ( 9 )
Now, taking R.H.S;
f ( e 2 t cos 3 t ) = f ( cos 3 t ) S S 2
f cos 3 t = s s 2 + k 2
Is the same way
f ( cos 3 t ) S S 2 = s s 2 + 3 2 S S 2 = s 2 ( 5 2 ) 2 + 9 = 5 2 5 2 13 45 ( 6 )
from (9) and (6) in epuation (1);
Solution: 2 5 2 3 + 5 2 5 2 13 45

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