What is inverse oflaplace (3(s+1))/(s^2+1/2) ?

The answer to inverse oflaplace (3(s+1))/(s^2+1/2) is 3(cos(sqrt(1/2)t)+sqrt(2)sin(sqrt(1/2)t))

inverse oflaplace (3(s+1))/(s^2+1/2)

inverse laplace

\frac{3 ( s + 1 )}{s ^{2} + \frac{1}{2}}

3 (cos (\frac{1}{2} t) + 2 sin (\frac{1}{2} t))

Solution steps

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

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

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

= 3 (cos (\frac{1}{2} t) + 2 sin (\frac{1}{2} t))

t a y l or e^{- \frac{x}{2}}, 0

n = 2 \sum \infty (\frac{1}{2})^{3 n}

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

\frac{d}{d x} (e^{c o s (x)} + cos (e^{x}))

d er i v a t i v e (1 + cos^{2} (x))^{3}

What is inverse oflaplace (3(s+1))/(s^2+1/2) ?
The answer to inverse oflaplace (3(s+1))/(s^2+1/2) is 3(cos(sqrt(1/2)t)+sqrt(2)sin(sqrt(1/2)t))