laplacetransform e^tsin(2t)

解答

拉普拉斯变换

e^{t} sin (2 t)

\frac{2}{( s - 1 ) ^{2} + 4}

求解步骤

L {e^{t} sin (2 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^{t} sin (2 t) : f (t) = sin (2 t), a = 1

= L {sin (2 t)} (s - 1)

L {sin (2 t)} : \frac{2}{s ^{2} + 4}

= \frac{2}{( s - 1 ) ^{2} + 4}