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Evaluate L{sin at/t}

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Evaluate L{sin at/t}

Posted by Mohit Mehra 4 years ago

CBSE > Class 12 > Applied Maths

1 answers

Arjűņ _Pāwåř 4 years ago

This is from laplace transform- L{sinat}=s2s2+a2[−e−st(1ssinat+as2cosat)]t=∞t=0L{sin⁡at}=s2s2+a2[−e−st(1ssin⁡at+as2cos⁡at)]t=0t=∞ L{sinat}=∫→+∞0e−stsinatdtL{sin⁡at}=∫0→+∞e−stsin⁡atdt I=∫→+∞0e−stsinat=12i∫→+∞0e−st(eiat−e−iat)dt=12i∫→+∞0(e−t(−ia+s)−e−t(ia+s)dtI=∫0→+∞e−stsin⁡at=12i∫0→+∞e−st(eiat−e−iat)dt=12i∫0→+∞(e−t(−ia+s)−e−t(ia+s)dt 2iI=∣∣∣e−t(−ia+s)(ia−s)∣∣∣∞0+∣∣∣e−t(ia+s)(ia+s)∣∣∣∞02iI=|e−t(−ia+s)(ia−s)|0∞+|e−t(ia+s)(ia+s)|0∞ 2iI=1(s−ia)−1(s+ia)2iI=1(s−ia)−1(s+ia) I=as2+a2 May be it will help you.. I did as i can... Thanks!

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