What is inverse oflaplace (E/L)/((s^2+1/(CL))) ?

The answer to inverse oflaplace (E/L)/((s^2+1/(CL))) is (Esqrt(C)sin(sqrt(1/(LC))t))/(sqrt(L))

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inverse oflaplace (E/L)/((s^2+1/(CL)))

inverse laplace

\frac{\frac{E}{L}}{( s ^{2} + \frac{1}{C L} )}

\frac{E C sin ( \frac{1}{L C} t )}{L}

Solution steps

L^{- 1} {\frac{\frac{E}{L}}{( s ^{2} + \frac{1}{L C} )}}

= L^{- 1} ⎩ ⎨ ⎧ \frac{E C}{L} \cdot \frac{\frac{1}{L C}}{s ^{2} + ( \frac{1}{L C} ) ^{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{E C}{L} L^{- 1} ⎩ ⎨ ⎧ \frac{\frac{1}{L C}}{s ^{2} + ( \frac{1}{L C} ) ^{2}} ⎭ ⎬ ⎫

Use Inverse Laplace Transform table:

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

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

= \frac{E C}{L} sin (\frac{1}{L C} t)

= \frac{E C sin ( \frac{1}{L C} t )}{L}

y = x^{π}

f (x) = \frac{x}{( 7 x - 6 ) ^{6}}, at x = 1

\frac{\partial}{\partial x} (3000 + \frac{400}{x + 3})

\frac{d}{d x} (\frac{x}{x ^{2} + 169})

y = x^{x^{3}}

What is inverse oflaplace (E/L)/((s^2+1/(CL))) ?
The answer to inverse oflaplace (E/L)/((s^2+1/(CL))) is (Esqrt(C)sin(sqrt(1/(LC))t))/(sqrt(L))