What is inverse oflaplace (56s)/(s^2+196) ?

The answer to inverse oflaplace (56s)/(s^2+196) is 56cos(14t)

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inverse oflaplace (56s)/(s^2+196)

inverse laplace

\frac{56 s}{s ^{2} + 196}

56 cos (14 t)

Solution steps

L^{- 1} {\frac{56 s}{s ^{2} + 196}}

Apply inverse transform rule:

L^{- 1} {F (s)} = f (t)

then

L^{- 1} {s F (s)} = \frac{d}{d t} f (t) + f (0)

For

\frac{56 s}{s ^{2} + 196} : F (s) = \frac{56}{s ^{2} + 196}

= \frac{d}{d t} (L^{- 1} {\frac{56}{s ^{2} + 196}}) + L^{- 1} {\frac{56}{s ^{2} + 196}} (0)

L^{- 1} {\frac{56}{s ^{2} + 196}} : 4 sin (14 t)

\frac{d}{d t} (4 sin (14 t)) = 56 cos (14 t)

Evaluate

4 sin (14 t)

at point

0 = 0

= 56 cos (14 t)

\frac{d y}{d x} = - 2 x tan (y), y (0) = \frac{π}{2}

\frac{d x}{d t} = x (1 - 0.0004 x)

\int_{1}^{2} 9 \frac{ln ( x )}{x ^{2}} d x

\int \frac{1}{x ( x + 1 )} d x

f (x) = x - 1, (10, 3)

What is inverse oflaplace (56s)/(s^2+196) ?
The answer to inverse oflaplace (56s)/(s^2+196) is 56cos(14t)