Question

Evaluate , L^{-1}left { frac{1}{(s+1)(s^2+1)} ight },using convolution theorem. 

21 Mar 2023
Answer :
Word Count : 258

To evaluateL^{-1} {1/[(s+1)(s^2+1)]} using the convolution theorem, we need to find the inverse Laplace transform of 1/[(s+1)(s^2+1)].

We can use partial fraction decomposition to write:

1/[(s+1)(s^2+1)] = A/(s+1) + (Bs + C)/(s^2+1)

Multiplying both sides by (s+1)(s^2+1), we get:

1 = A(s^2+1) + (Bs+C)(s+1)

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