What is laplacetransform 5sin(7t) ?

The answer to laplacetransform 5sin(7t) is (35)/(s^2+49)

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laplacetransform 5sin(7t)

laplace transform

5 sin (7 t)

\frac{35}{s ^{2} + 49}

Solution steps

L {5 sin (7 t)}

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 (7 t)}

L {sin (7 t)} : \frac{7}{s ^{2} + 49}

= 5 \cdot \frac{7}{s ^{2} + 49}

Refine

5 \frac{7}{s ^{2} + 49} : \frac{35}{s ^{2} + 49}

= \frac{35}{s ^{2} + 49}

y^{^{'''}} - 3 y^{^{''}} - 4 y^{^{'}} = 0

f (t) = 106 - 80 e^{- 0.4 t}

\int 3^{x} d x

2 + 3 + cos^{2} (x)

\int \frac{2}{x ^{4}} d x

What is laplacetransform 5sin(7t) ?
The answer to laplacetransform 5sin(7t) is (35)/(s^2+49)