laplacetransform cos(2(t-pi/2))

解

ラプラス変換

cos (2 (t - \frac{π}{2}))

- \frac{s}{s ^{2} + 4}

解答ステップ

L {cos (2 (t - \frac{π}{2}))}

ラプラス変換表を使用する:

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

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

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

= - \frac{s}{s ^{2} + 4}