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Popular >

inverse oflaplace (e^{-spi})/(s^2+2s+2)

Solution

inverse laplace

\frac{e ^{- s π}}{s ^{2} + 2 s + 2}

Solution

H (t - π) e^{- t + π} sin (t - π)

Solution steps

L^{- 1} {\frac{e ^{- π s}}{s ^{2} + 2 s + 2}}

Apply inverse transform rule:

if

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

then

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

Where

H (t)

is Heaviside step function

= H (t - π) L^{- 1} {\frac{1}{s ^{2} + 2 s + 2}} (t - π)

L^{- 1} {\frac{1}{s ^{2} + 2 s + 2}} : e^{- t} sin (t)

= H (t - π) e^{- (t - π)} sin (t - π)

= H (t - π) e^{- t + π} sin (t - π)

Popular Examples

integral of 7csc(x)

\int 7 csc (x) d x

derivative of 2x-6

\frac{d}{d x} (2 x - 6)

sum from n=1 to infinity of n/(9+n)

n = 1 \sum \infty \frac{n}{9 + n}

derivative of (9e^{9x})/(8x+3)derivative of

\frac{9 e ^{9 x}}{8 x + 3}

integral of-x^2+8x

\int - x^{2} + 8 x d x

Frequently Asked Questions (FAQ)

What is inverse oflaplace (e^{-spi})/(s^2+2s+2) ?
The answer to inverse oflaplace (e^{-spi})/(s^2+2s+2) is \H(t-pi)e^{-t+pi}sin(t-pi)