What is laplacetransform 5sin(5t)sin(100t) ?

The answer to laplacetransform 5sin(5t)sin(100t) is -(5s)/(2(s^2+11025))+(5s)/(2(s^2+9025))

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laplacetransform 5sin(5t)sin(100t)

laplace transform

5 sin (5 t) sin (100 t)

- \frac{5 s}{2 ( s ^{2} + 11025 )} + \frac{5 s}{2 ( s ^{2} + 9025 )}

Solution steps

L {5 sin (5 t) sin (100 t)}

Rewrite using trig identities

L {- \frac{5}{2} cos (105 t) + \frac{5}{2} cos (- 95 t)}

Use the linearity property of Laplace Transform:

For functions

f (t), g (t)

and constants

a, b : L {a \cdot f (t) + b \cdot g (t)} = a \cdot L {f (t)} + b \cdot L {g (t)}

= - \frac{5}{2} L {cos (105 t)} + \frac{5}{2} L {cos (- 95 t)}

L {cos (105 t)} : \frac{s}{s ^{2} + 11025}

L {cos (- 95 t)} : \frac{s}{s ^{2} + 9025}

= - \frac{5}{2} \cdot \frac{s}{s ^{2} + 11025} + \frac{5}{2} \cdot \frac{s}{s ^{2} + 9025}

Refine

- \frac{5}{2} \frac{s}{s ^{2} + 11025} + \frac{5}{2} \frac{s}{s ^{2} + 9025} : - \frac{5 s}{2 ( s ^{2} + 11025 )} + \frac{5 s}{2 ( s ^{2} + 9025 )}

= - \frac{5 s}{2 ( s ^{2} + 11025 )} + \frac{5 s}{2 ( s ^{2} + 9025 )}

\frac{6 t + 1}{6 t - 1}

x \to 0 lim (\frac{2 x ^{2} + 3 x}{x})

\frac{6 s + 6}{2 s ^{2} + 1}

y^{^{'}} e^{9 x} = 0

y^{^{'}} + 2 y - y^{2} = 0

What is laplacetransform 5sin(5t)sin(100t) ?
The answer to laplacetransform 5sin(5t)sin(100t) is -(5s)/(2(s^2+11025))+(5s)/(2(s^2+9025))