What is inverse oflaplace (1/7)/(s^2+19980/7) ?

The answer to inverse oflaplace (1/7)/(s^2+19980/7) is 1/(6sqrt(3885))sin((6sqrt(555)t)/(sqrt(7)))

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inverse oflaplace (1/7)/(s^2+19980/7)

inverse laplace

\frac{\frac{1}{7}}{s ^{2} + \frac{19980}{7}}

\frac{1}{6 3885} sin (\frac{6 555 t}{7})

Solution steps

L^{- 1} {\frac{\frac{1}{7}}{s ^{2} + \frac{19980}{7}}}

= L^{- 1} ⎩ ⎨ ⎧ \frac{1}{6 3885} \cdot \frac{\frac{6 555}{7}}{s ^{2} + ( \frac{6 555}{7} ) ^{2}} ⎭ ⎬ ⎫

Use the constant multiplication property of Inverse Laplace Transform:

For function

f (t)

and constant

a : L^{- 1} {a \cdot f (t)} = a \cdot L^{- 1} {f (t)}

= \frac{1}{6 3885} L^{- 1} ⎩ ⎨ ⎧ \frac{\frac{6 555}{7}}{s ^{2} + ( \frac{6 555}{7} ) ^{2}} ⎭ ⎬ ⎫

Use Inverse Laplace Transform table:

L^{- 1} {\frac{a}{s ^{2} + a ^{2}}} = sin (a t)

L^{- 1} {\frac{\frac{6 555}{7}}{s ^{2} + ( \frac{6 555}{7} ) ^{2}}} = sin (\frac{6 555}{7} t)

= \frac{1}{6 3885} sin (\frac{6 555}{7} t)

= \frac{1}{6 3885} sin (\frac{6 555 t}{7})

\int t^{- \frac{1}{2}} (t^{4} + 2 t^{2} - 1) d t

\int sin (s) d s

- 4 t^{2} + 16 t + 9

\frac{\partial}{\partial x} (4 x (2 + y)^{- 1})

f (x) = \frac{x}{1 + x ^{2}}, at x = 2

What is inverse oflaplace (1/7)/(s^2+19980/7) ?
The answer to inverse oflaplace (1/7)/(s^2+19980/7) is 1/(6sqrt(3885))sin((6sqrt(555)t)/(sqrt(7)))