laplacetransform sin(2t+pi/4)

解

ラプラス変換

sin (2 t + \frac{π}{4})

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

解答ステップ

L {sin (2 t + \frac{π}{4})}

ラプラス変換表を使用する:

L {sin (a t + b)} = \frac{s \cdot sin ( b ) + a \cdot cos ( b )}{s ^{2} + a ^{2}}

L {sin (2 t + \frac{π}{4})} = \frac{s sin ( \frac{π}{4} ) + 2 cos ( \frac{π}{4} )}{s ^{2} + 2 ^{2}}

= \frac{s sin ( \frac{π}{4} ) + 2 cos ( \frac{π}{4} )}{s ^{2} + 2 ^{2}}

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