laplacetransform cos(t-1)

解

ラプラス変換

cos (t - 1)

\frac{cos ( 1 ) s + sin ( 1 )}{s ^{2} + 1}

解答ステップ

L {cos (t - 1)}

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 (t - 1)} = \frac{s cos ( - 1 ) - 1 \cdot sin ( - 1 )}{s ^{2} + 1 ^{2}}

= \frac{s cos ( - 1 ) - 1 \cdot sin ( - 1 )}{s ^{2} + 1 ^{2}}

= \frac{cos ( 1 ) s + sin ( 1 )}{s ^{2} + 1}