Find the inverse Laplace transform of F(s)=frac{(s+4)}{(s^2+9)} a)cos(t)+frac{4}{3}sin(t) b)non of the above c) cos(3t)+sin(3t) d) cos(3t)+frac{4}{3} sin(3t) e)cos(3t)+frac{2}{3} sin(3t) f) cos(t)+4sin(t)

sjeikdom0 2021-02-08 Answered
Find the inverse Laplace transform of F(s)=(s+4)(s2+9)
a)cos(t)+43sin(t)
b)non of the above
c) cos(3t)+sin(3t)
d) cos(3t)+43sin(3t)
e)cos(3t)+23sin(3t)
f) cos(t)+4sin(t)
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Expert Answer

d2saint0
Answered 2021-02-09 Author has 89 answers
Step 1
The given function is F(s)=(s+4)(s2+9)
The following formulae are used in finding the inverse laplace transform of the given function.
L1{f(s)+g(s)}=L1{f(t)}+L1{g(t)}
L1{af(s)}=aL1{f(t)}
L1{s(s2+a2)}=cosat
L1{1(s2+a2)}=sinat
Step 2
Evaluate the inverse laplace transform of the given function as follows.
L1{s+4s2+9}=L1{s(s2+9)}+L1{4(s2+9)}
=L1{s(s2+32)}+4L1{1(s2+32)}
=cos3t+4(13sin3t)
=cos3t+43sin3t
Therefore, the inverse Laplace transform of the given function is cos3t+43sin3t
Thus, the correct option is (d).
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