laplacetransform cos(25pit+pi/2)

解

ラプラス変換

cos (25 π t + \frac{π}{2})

- \frac{25 π}{s ^{2} + 625 π ^{2}}

解答ステップ

L {cos (25 π 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 (25 π t + \frac{π}{2})} = \frac{s cos ( \frac{π}{2} ) - 25 π sin ( \frac{π}{2} )}{s ^{2} + ( 25 π ) ^{2}}

= \frac{s cos ( \frac{π}{2} ) - 25 π sin ( \frac{π}{2} )}{s ^{2} + ( 25 π ) ^{2}}

= - \frac{25 π}{s ^{2} + 625 π ^{2}}