What is laplacetransform sin(2t+pi/4) ?

The answer to laplacetransform sin(2t+pi/4) is (s+2)/(sqrt(2)(s^2+4))

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laplacetransform sin(2t+pi/4)

laplace transform

sin (2 t + \frac{π}{4})

\frac{s + 2}{2 ( s ^{2} + 4 )}

Solution steps

L {sin (2 t + \frac{π}{4})}

Use Laplace Transform table:

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

L {sin (2 t + \frac{π}{4})} = \frac{s sin ( \frac{π}{4} ) + 2 cos ( \frac{π}{4} )}{s ^{2} + 2 ^{2}}

= \frac{s sin ( \frac{π}{4} ) + 2 cos ( \frac{π}{4} )}{s ^{2} + 2 ^{2}}

= \frac{s + 2}{2 ( s ^{2} + 4 )}

\int (5 x + 2) d x

y^{^{''}} + 8 y^{^{'}} + 32 y = 0, y (0) = 0, y^{^{'}} (0) = 0

\int \frac{- x}{1 - x ^{2}} d x

\frac{d}{d x} (c x e^{- 2 x})

\frac{d}{d x} (\frac{2 sin ( x )}{x})

What is laplacetransform sin(2t+pi/4) ?
The answer to laplacetransform sin(2t+pi/4) is (s+2)/(sqrt(2)(s^2+4))