laplacetransform sin(6(t-(3pi)/6))

解

ラプラス変換

sin (6 (t - \frac{3 π}{6}))

- \frac{6}{s ^{2} + 36}

解答ステップ

L {sin (6 (t - \frac{3 π}{6}))}

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 (6 (t - \frac{3 π}{6}))} = \frac{s sin ( - 3 π ) + 6 cos ( - 3 π )}{s ^{2} + 6 ^{2}}

= \frac{s sin ( - 3 π ) + 6 cos ( - 3 π )}{s ^{2} + 6 ^{2}}

= - \frac{6}{s ^{2} + 36}