laplacetransform t+sin(t)

解答

拉普拉斯变换

t + sin (t)

\frac{1}{s ^{2}} + \frac{1}{s ^{2} + 1}

求解步骤

L {t + sin (t)}

利用拉普拉斯变换的线性特性:

对于函数

f (t), g (t)

和常数

a, b : L {a \cdot f (t) + b \cdot g (t)} = a \cdot L {f (t)} + b \cdot L {g (t)}

= L {t} + L {sin (t)}

L {t} : \frac{1}{s ^{2}}

L {sin (t)} : \frac{1}{s ^{2} + 1}

= \frac{1}{s ^{2}} + \frac{1}{s ^{2} + 1}

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