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The Laplace transform of the given wave as shown below is—
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A· e– πs – 1 (s2 + 1) -
A· e– πs + 1 (s2 + 1) -
A· eπs – 1 (s2 + 1) -
A· eπs + 1 (s2 + 1)
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Correct Option: B
The function for the given waveform is
f(t) = A sin t for 0 < t < π
= 0, for t > π
By definition, we have
L{f(t)} = ∫∞0 f(t)e– stdt
= ∫π0 A sin t e– stdt
= A ∫π0 sin t e– stdt
| = | [e– st(– s sin t – cos t)]π0 | (s2 + 1) |
| = A | (s2+ 1) |
Hence, alternative (B) is the correct choice.
