What is laplacetransform sin(3t-1/2) ?

The answer to laplacetransform sin(3t-1/2) is (-sin(1/2)s+3cos(1/2))/(s^2+9)

Popular >

laplacetransform sin(3t-1/2)

laplace transform

sin (3 t - \frac{1}{2})

\frac{- sin ( \frac{1}{2} ) s + 3 cos ( \frac{1}{2} )}{s ^{2} + 9}

Solution steps

L {sin (3 t - \frac{1}{2})}

Use Laplace Transform table:

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

L {sin (3 t - \frac{1}{2})} = \frac{s sin ( - \frac{1}{2} ) + 3 cos ( - \frac{1}{2} )}{s ^{2} + 3 ^{2}}

= \frac{s sin ( - \frac{1}{2} ) + 3 cos ( - \frac{1}{2} )}{s ^{2} + 3 ^{2}}

= \frac{- sin ( \frac{1}{2} ) s + 3 cos ( \frac{1}{2} )}{s ^{2} + 9}

x \to 0 lim (\frac{sin ^{4} ( x )}{x})

\frac{d}{d x} (2500 - x^{2})

\int_{0}^{1} t^{2} e^{- 2 t} d t

\int \frac{e ^{x}}{( e ^{x} - 6 ) ( e ^{2 x} + 1 )} d x

f (x) = \frac{1 - ln ( x )}{x ^{2}}

What is laplacetransform sin(3t-1/2) ?
The answer to laplacetransform sin(3t-1/2) is (-sin(1/2)s+3cos(1/2))/(s^2+9)