Evaluate L^(-1)(frac(3x)(x^2+9)) where L^(-1) is inverse Laplace transformation?a)2 cos(2x) (b)3 sin(3x)(c)3 cos(9x)(d)3 cos(3x)(e)2 cos(3x)

Reeves

Reeves

Answered question

2021-09-15

Evaluate L1(3xx2+9) where L1 is inverse Laplace transformation?
a)2cos(2x)
b)3sin(3x)
c)3cos(9x)
d)3cos(3x)
e)2cos(3x)

Answer & Explanation

broliY

broliY

Skilled2021-09-16Added 97 answers

Step 1
we have to evaluate:
L1(3xx2+9)
where L1 is the inverse laplace transformation.
Step 2
L1(3xx2+9)=3L1(xx2+9)
=3L1(xx2+32)
as we know that:
L1(ss2+a2)=cos(at)
therefore,
L1(3xx2+9)=3L1(xx2+32)
=3cos(3x)
therefore, L1(3xx2+9)=3cos(3x)
Step 3
therefore the option (d) is correct.

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