laplacetransform sin(100t+30)

解答

拉普拉斯变换

sin (100 t + 30)

\frac{sin ( 30 ) s + 100 cos ( 30 )}{s ^{2} + 10000}

求解步骤

L {sin (100 t + 30)}

使用拉普拉斯变换表:

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

L {sin (100 t + 30)} = \frac{s sin ( 30 ) + 100 cos ( 30 )}{s ^{2} + 10 0 ^{2}}

= \frac{s sin ( 30 ) + 100 cos ( 30 )}{s ^{2} + 10 0 ^{2}}

= \frac{sin ( 30 ) s + 100 cos ( 30 )}{s ^{2} + 10000}

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