laplacetransform (t^2+1/2)^2

解

ラプラス変換

(t^{2} + \frac{1}{2})^{2}

\frac{24}{s ^{5}} + \frac{2}{s ^{3}} + \frac{1}{4 s}

解答ステップ

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

拡張

(t^{2} + \frac{1}{2})^{2} : t^{4} + t^{2} + \frac{1}{4}

= L {t^{4} + t^{2} + \frac{1}{4}}

ラプラス変形の線形性を使用する:

関数

f (t), g (t)

と定数

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

= L {t^{4}} + L {t^{2}} + L {\frac{1}{4}}

L {t^{4}} : \frac{24}{s ^{5}}

L {t^{2}} : \frac{2}{s ^{3}}

L {\frac{1}{4}} : \frac{1}{4 s}

= \frac{24}{s ^{5}} + \frac{2}{s ^{3}} + \frac{1}{4 s}