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

The answer to inverse oflaplace 1/((s^2+1)^2) is 1/2 (sin(t)-tcos(t))

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

inverse laplace

\frac{1}{( s ^{2} + 1 ) ^{2}}

\frac{1}{2} (sin (t) - t cos (t))

Solution steps

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

= L^{- 1} {\frac{1}{2} \cdot \frac{2 \cdot 1 ^{3}}{( s ^{2} + 1 ^{2} ) ^{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}{2} L^{- 1} {\frac{2 \cdot 1 ^{3}}{( s ^{2} + 1 ^{2} ) ^{2}}}

Use Inverse Laplace Transform table:

L^{- 1} {\frac{2 a ^{3}}{( s ^{2} + a ^{2} ) ^{2}}} = sin (a t) - a t cos (a t)

L^{- 1} {\frac{2 \cdot 1 ^{3}}{( s ^{2} + 1 ^{2} ) ^{2}}} = sin (t) - t cos (t)

= \frac{1}{2} (sin (t) - t cos (t))

\frac{x ^{2}}{7 + 8 x}

\frac{d}{d x} (3 x^{4} (4 - x)^{3})

\int \frac{8}{( 1 + 4 t ) ^{2}} d t

\frac{d}{d x} (8 + x)

f (x) = ln (x), at x = 6

What is inverse oflaplace 1/((s^2+1)^2) ?
The answer to inverse oflaplace 1/((s^2+1)^2) is 1/2 (sin(t)-tcos(t))