Question

The Laplace inverse of L^{-1}left[frac{s}{s^2+5^2}right] is a) cos(5t) b) sin h(5t) c) sin(5t) d) cos h(5t)

Laplace transform
ANSWERED
asked 2020-12-30
The Laplace inverse of \(L^{-1}\left[\frac{s}{s^2+5^2}\right]\) is
\(a) \cos(5t)\)
\(b) \sin h(5t)\)
\(c) \sin(5t)\)
\(d) \cos h(5t)\)

Answers (1)

2020-12-31
Step 1
To find the Laplace transformation of \(L^{-1}\left[\frac{s}{s^2+5^2}\right]\)
Solution:
let \(\varphi(s)\) be the function whose Laplace transformation will be \(\frac{s}{s^2+5^2}\)
So,
\(L(\varphi(s))=\frac{s}{s^2+5^2}\)
Applying inverse we get,
\(\varphi(s)=L^{-1}\left[\frac{s}{s^2+5^2}\right] \dots(1)\)
Step 2
since, we know that
\(L(\cos as)=\frac{s}{s^2+a^2}\)
\(\text{and } (\cos as)=L^{-1}\left(\frac{s}{s^2+a^2}\right)\)
From equation (1),
\(\cos(5s)=\frac{s}{s^2+5^2}\)
Hence, the inverse Laplace for given expression is cos5t.
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