What is laplacetransform 5sin(3t-pi/4) ?

The answer to laplacetransform 5sin(3t-pi/4) is (5(-s+3))/(sqrt(2)(s^2+9))

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laplacetransform 5sin(3t-pi/4)

laplace transform

5 sin (3 t - \frac{π}{4})

\frac{5 ( - s + 3 )}{2 ( s ^{2} + 9 )}

Solution steps

L {5 sin (3 t - \frac{π}{4})}

Use the constant multiplication property of Laplace Transform:

For function

f (t)

and constant

a : L {a \cdot f (t)} = a \cdot L {f (t)}

= 5 L {sin (3 t - \frac{π}{4})}

L {sin (3 t - \frac{π}{4})} : \frac{- s + 3}{2 ( s ^{2} + 9 )}

= 5 \cdot \frac{- s + 3}{2 ( s ^{2} + 9 )}

Refine

5 \frac{- s + 3}{2 ( s ^{2} + 9 )} : \frac{5 ( - s + 3 )}{2 ( s ^{2} + 9 )}

= \frac{5 ( - s + 3 )}{2 ( s ^{2} + 9 )}

e^{x}, e^{- x}, [0, 1]

\frac{\partial}{\partial x} ((x^{3} - y^{2})^{- 1})

x \to 0 + lim ((1 + x)^{(\frac{1}{x})})

\frac{d}{d x} (25 x^{3} - 6 x^{2} + 7 x - 88)

\frac{d y}{d x} = 0.1 y (1 - \frac{y}{500})

What is laplacetransform 5sin(3t-pi/4) ?
The answer to laplacetransform 5sin(3t-pi/4) is (5(-s+3))/(sqrt(2)(s^2+9))