Question

What is natural frequency, and damping ratio, ? of the below equation

Answer 1

\[\zeta = (damping~ratio)~and ~ \omega_n = naturl frequency\]

Answer 2

\[\large G(s) = \frac {36} {s^2 + 5s + 36} \] @ganeshie8 ?

Answer 3

no clue with laplaces sorry @eliassaab

Answer 4

all good, cheers man

Answer 5

Complete the square in the denominator to obtain
\[\Large
\mathcal{L}_s^{-1}\left[\frac{36}{s^2+5 s+36}\right](t)=\frac{72
e^{-\frac{5 t}{2}} \sin \left(\frac{\sqrt{119}
t}{2}\right)}{\sqrt{119}}
\]

Answer 6

Completing the square in the denominator is done as follows:
\[
s^2+5 s+36=s^2+5
s+\frac{25}{4}-\frac{25}{4}+36=\left(s+\frac{5}{2}\right)^2+\frac{119}{
4}=\\
\left(s+\frac{5}{2}\right)^2+\left(\frac{\sqrt{119}}{
2}\right)^2

\]

Answer 7

From the solution, you can read the damping and the frequency
damping = 5/2
\[

w_n=\frac{\sqrt {119}}{2}
\]

Answer 8

@ganeshie8

Answer 9

holy WOW dude! @eliassaab
thanks for that man, i think i'll need an hour before I understand this though
cheers again!

Answer 10

yw