laplacetransform e^{-5t}sin(7t)

解答

拉普拉斯变换

e^{- 5 t} sin (7 t)

\frac{7}{( s + 5 ) ^{2} + 49}

求解步骤

L {e^{- 5 t} sin (7 t)}

应用变换法则: if

L {f (t)} = F (s)

则

L {e^{a t} f (t)} = F (s - a)

对于

e^{- 5 t} sin (7 t) : f (t) = sin (7 t), a = - 5

= L {sin (7 t)} (s + 5)

L {sin (7 t)} : \frac{7}{s ^{2} + 49}

= \frac{7}{( s + 5 ) ^{2} + 49}

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