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)

Armorikam 2020-12-30 Answered
The Laplace inverse of L1[ss2+52] is
a)cos(5t)
b)sinh(5t)
c)sin(5t)
d)cosh(5t)
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Expert Answer

oppturf
Answered 2020-12-31 Author has 94 answers
Step 1
To find the Laplace transformation of L1[ss2+52]
Solution:
let φ(s) be the function whose Laplace transformation will be ss2+52
So,
L(φ(s))=ss2+52
Applying inverse we get,
φ(s)=L1[ss2+52](1)
Step 2
since, we know that
L(cosas)=ss2+a2
and (cosas)=L1(ss2+a2)
From equation (1),
cos(5s)=ss2+52
Hence, the inverse Laplace for given expression is cos5t.
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