Differential equations

**lvleph** · December 3rd 2009, 09:33 AM

Originally Posted by Apprentice123

Ok. Please look at this site, the imaginary part is different, you know why?

What site?

**Apprentice123** · December 3rd 2009, 09:35 AM

Originally Posted by lvleph

What site?

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

**Apprentice123** · December 3rd 2009, 11:44 AM

Someone got the imaginary part in problem of th site?

**lvleph** · December 3rd 2009, 11:50 AM

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.

**Apprentice123** · December 3rd 2009, 12:55 PM

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?

**lvleph** · December 3rd 2009, 01:03 PM

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
$w_2 = \frac{-c}{2m} - \frac{\sqrt{-c^2 + 4mk}}{2m} i$ .

**Apprentice123** · December 4th 2009, 04:07 AM

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 $c^2 > 4mk$ ?

**lvleph** · December 4th 2009, 05:10 AM

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 $c^2 - 4mk$ .

**Apprentice123** · December 4th 2009, 11:18 AM

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

**Apprentice123** · December 6th 2009, 02:14 PM

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

**lvleph** · December 6th 2009, 04:36 PM

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

**Apprentice123** · December 7th 2009, 03:56 AM

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

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