Question
The Laplace transform of function f(t) is L(t) = 1 ( s 2 + ω 2 ) . Then, f(t) is
Options :
f ( t ) = 1 ω 2 ( 1 − cos ω t )
f ( t ) = 1 ω cos ω t
f ( t ) = 1 ω sin ω t
f ( t ) = 1 ω 2 ( 1 − sin ω t )
Answer :
Solution :
L ( sin a t ) = a s 2 + a 2
Similarly,
L ( sin ω t ) = ω s 2 + ω 2
∴ L − 1 ( 1 s 2 + ω 2 ) = sin ω t ω = f ( t )
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