What is inverse oflaplace (28)/((s^2+11)) ?

The answer to inverse oflaplace (28)/((s^2+11)) is (28)/(sqrt(11))sin(sqrt(11)t)

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inverse oflaplace (28)/((s^2+11))

inverse laplace

\frac{28}{( s ^{2} + 11 )}

\frac{28}{11} sin (11 t)

Solution steps

L^{- 1} {\frac{28}{( s ^{2} + 11 )}}

= L^{- 1} {\frac{28}{11} \cdot \frac{11}{s ^{2} + ( 11 ) ^{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{28}{11} L^{- 1} {\frac{11}{s ^{2} + ( 11 ) ^{2}}}

Use Inverse Laplace Transform table:

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

L^{- 1} {\frac{11}{s ^{2} + ( 11 ) ^{2}}} = sin (11 t)

= \frac{28}{11} sin (11 t)

x \to 1 lim (3 x^{4} + 3 x^{2} - x + 2)

\frac{d ^{2} y}{d t ^{2}} - 5 \frac{d y}{d t} + 6 y = 0

\frac{\partial}{\partial x} (ln (x^{5} + y^{5}))

e^{- 1 (t + 1)}

\int e^{0.5 x} d x

What is inverse oflaplace (28)/((s^2+11)) ?
The answer to inverse oflaplace (28)/((s^2+11)) is (28)/(sqrt(11))sin(sqrt(11)t)