# Thread: Differential equations

1. Originally Posted by Apprentice123
Ok. Please look at this site, the imaginary part is different, you know why?
What site?

2. Originally Posted by lvleph
What site?

I forgot to put the link, sorry
http://www.stewartcalculus.com/data/...Orders_Stu.pdf

3. Someone got the imaginary part in problem of th site?

4. They probably wrote the imaginary part as
$\frac{\sqrt{-c^2 + 4mk}}{2m}$
This is actually correct since the imaginary pary is not going to have the $i = \sqrt{-1}$. Thus we have to factor this out of the determinant.

5. Originally Posted by lvleph
They probably wrote the imaginary part as
$\frac{\sqrt{-c^2 + 4mk}}{2m}$
This is actually correct since the imaginary pary is not going to have the $i = \sqrt{-1}$. Thus we have to factor this out of the determinant.
If we have $c^2 > 4mk$ we has $\sqrt{-1}$ or am I wrong?

6. No we have to have $4mk > c^2$ If that is the case then
$w_1 = \frac{-c}{2m} + \frac{\sqrt{-c^2 + 4mk}}{2m} i$
and
$w_2 = \frac{-c}{2m} - \frac{\sqrt{-c^2 + 4mk}}{2m} i$.

7. Originally Posted by lvleph
No we have to have $4mk > c^2$ If that is the case then
$w_1 = \frac{-c}{2m} + \frac{\sqrt{-c^2 + 4mk}}{2m} i$
and
$w_2 = \frac{-c}{2m} - \frac{\sqrt{-c^2 + 4mk}}{2m} i$.

Not have $c^2 > 4mk$ ?

8. If $c^2>4mk$ the solution would not be imaginary. Notice the way I have it written already assumes that we have an imaginary solution, and I have factored out the $i$. That is why it is $-c^2 + 4mk$ instead of $c^2 - 4mk$.

9. Originally Posted by lvleph
If $c^2>4mk$ the solution would not be imaginary. Notice the way I have it written already assumes that we have an imaginary solution, and I have factored out the $i$. That is why it is $-c^2 + 4mk$ instead of $c^2 - 4mk$.
Sorry my confusion. Thanks

10. Can you help me or have any stuff about Mechanical Vibrations: Beats and Resonance

11. Do a google book search. I don't know much about mechanical vibration.

12. Originally Posted by lvleph
Do a google book search. I don't know much about mechanical vibration.

I did not find material to calculate the equations and I still do not understand mechanical vibration

Page 4 of 4 First 1234