laplacetransform 5sin(3t-pi/4)

解

ラプラス変換

5 sin (3 t - \frac{π}{4})

\frac{5 ( - s + 3 )}{2 ( s ^{2} + 9 )}

解答ステップ

L {5 sin (3 t - \frac{π}{4})}

ラプラス変換の定数乗法を使用する:

関数 f(t) と定数

a : L {a \cdot f (t)} = a \cdot L {f (t)}

= 5 L {sin (3 t - \frac{π}{4})}

L {sin (3 t - \frac{π}{4})} : \frac{- s + 3}{2 ( s ^{2} + 9 )}

= 5 \cdot \frac{- s + 3}{2 ( s ^{2} + 9 )}

改良

5 \frac{- s + 3}{2 ( s ^{2} + 9 )} : \frac{5 ( - s + 3 )}{2 ( s ^{2} + 9 )}

= \frac{5 ( - s + 3 )}{2 ( s ^{2} + 9 )}