
i have stalled in another problem.
Given that when
Solving using partial fractions:
Therefore:
is the solution. however if i take the inverse of that does not match the solution.
can you spot where i have gone wrong ?

I seem to be making the same mistake again with this question:
Given that:
and when
Taking Laplace Transforms:
Now solving using partial fractions:
From which:
and
Hence:
The solution gives
What step am i missing out or where have i gone wrong ?

For
http://www.mathhelpforum.com/mathhe...8ee2743f1.gif
you don't need to use PFD write s^2 + 8 as s^2 + 4 + 4 and separate
Write as [(s^2+4)/[(s^2+4)(s^2+9)] + 4/[(s^2+4)(s^2+9)]
L(s) = 1/(s^2+9) + 4/(s^2+4)(s^2+9) both of which are standard transforms
y(t) = 1/3sin(3t) + 4[1/5*(1/3sin(3t)1/2sin(2t)]
= 1/3sin(3t)4/15sin(3t) + 2/5sin(2t)
= 1/15sin(3t) + 2/5sin(2t)

in general you are using the incorrect PFD
For an irreducible quadratic 1/(s^2+a) the term in the decomposition
is (As+B)/(s^2+a) not A/(s^2+a)
It is for linear factors1/(s+a) you have A/(s+a)
For linear factor1/[(sa)^n] include A1/(sa) +A2/(sa)^2 + ..........+ An/(sa)^n
For example for 1/s^2 you would have a A/s and a B/s^2 in the decomposition