partial fraction decomposition to find the inverse Laplace T

[xref228]

Use partial fraction decomposition to find the inverse Laplace Transforms of the following functions:
a)F(s) = 1 / s3-5s2
b)F(s) = s2-2s / s4 + 5s2 + 4

 

[galactus]

Re: partial fraction decomposition to find the inverse Lapla

Use partial fraction decomposition to find the inverse Laplace Transforms of the following functions:

a)F(s) = 1 / s3-5s2

Please use ^ (SHIFT 6) to represent exponents. You have \(\displaystyle \frac{1}{s^{3}}-5s^{2}\)

I assume you mean:

\(\displaystyle F(s)=\frac{1}{s^{3}-5s^{2}}=\frac{1}{25(s-5)}-\frac{1}{25s}-\frac{1}{25s^{2}}\)

Look them up in a LaPlace table.

i.e \(\displaystyle \frac{1}{s-a}=e^{at}\)

\(\displaystyle \frac{1}{s}=1\)

\(\displaystyle \frac{1}{s^{2}}=t\)

b)F(s) = s2-2s / s4 + 5s2 + 4

I assume this means \(\displaystyle \frac{s^{2}-2s}{s^{4}+5s^{2}+4}\)

Please use proper grouping symbols. Here is what you have written. Not to mention the lack of exponents.

\(\displaystyle s^{2}-\frac{2s}{s^{4}}+5s^{2}+4\)

Expand into a patial fraction and look up in a Laplace table.

\(\displaystyle \frac{2s}{3(s^{2}+4)}+\frac{4}{3(s^{2}+4)}-\frac{2s}{3(s^{2}+1)}-\frac{1}{3(s^{2}+1)}\)