Question

find the laplace tranform of S(A)​

Answer 1

Step-by-step explanation:

L{sinat}(s) = ∫→+∞0e−stsinatdt Definition of Laplace Transform

= limL→∞∫L0e−stsinatdt Definition of Improper Integral

= limL→∞[e−st(−ssinat−acosat)(−s)2+a2]L0 Primitive of eaxsinbx

= limL→∞(e−sL(−ssinaL−acosaL)s2+a2−e−s×0(−ssin(0×a)−acos(0×a))s2+a2)

= limL→∞(ssin0+acos0s2+a2−e−sL(ssinaL+acosaL)s2+a2) Exponential of Zero and rearranging

= ssin0+acos0s2+a2−0 Exponential Tends to Zero

= as2+a2 Sine of Zero is Zero, Cosine of Zero is One

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