find the inverse Laplace transform of the given function. {F}{left({s}right)}=frac{{{2}{s}-{3}}}{{{s}^{2}-{4}}}

floymdiT 2021-02-16 Answered
find the inverse Laplace transform of the given function.
F(s)=2s3s24
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Expert Answer

SabadisO
Answered 2021-02-17 Author has 108 answers
Step 1
Given function is:
F(s)=2s3s24
Since the Laplace transform of:
L(sinhat)=as2a2
And
L(coshat)=ss2a2
Step 2
Now,
Using the above transform:
F(s)=2s3s24
=2ss243s24
=2ss222322s222
=2L(cosh2t)32L(sinh2t)
=L(2cosh2t32sinh2t)
inverse Laplace transform of L(2cosh2t32sinh2t):
L1(L(2cosh2t32sinh2t))=2cosh2t32sinh2t
THEREFORE Inverse Laplace transform of given function is 2cosh2t32sinh2t
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