Question

Need help on how to simplify (8s^2-4s+12)/(s(s^2+4)) to (5 s-4)/(s^2+4) + 3/s

Answer 1

laplace?

Answer 2

yeah, I'm trying to do that right now, but I don't know how they simplified it to that..

Answer 3

First partial fractions, then complete the square, and then get clever and look for the right inverse transforms on the table.

Answer 4

Thanks! I figured it out. So the answer is \[3-2\sin2t+5\cos2t\] but i don't know how to get the 2sin2t..

Answer 5

this is a partial fraction
to solve the other part
5s-4/(s^2+4)+3s =5s-4/(s^2+3s+4)
by factorisation the denominator gives
(s-1)(s+4)
therefore 5s-4/(s-1)(s+4) which in turns gives A/(s-1) +B/(s+4)
and using cover up rule
the for A 5s-4/s+4 as s tends to 1
we have 5(1)-4/1+4=1/5
and for B 5s-4/s-1 as s tends to -4
gives -20-4/-4-5=-24/5
the substituting in the above
gives 1/5(s-1) -24/5(s+4)

Answer 6

8s^2-4s+12/s(s^2+4) =A/s+Bs+C/s^2+4
using partial fraction and collecting co effiecient
8s^2-4s+12=A(s^2+4)+s(Bs+C)
=As^2+4A+Bs^2+Cs
collecting co efficient
8s^2=s^2(A+B) equation 1
-4s=Cs equation 2
12=4A equation 3
then solving for the values
from equn 3
A=12/4=3
substituting values in equn 1
8=A+B
8=3+B
then B=5
and C=-4 from equn 2
then putting back all the values we have
3/s+5-4/s^2+4