# Rearranging equations with square roots...

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I'm trying to use the vibrational frequency equation to calculate the frequency constant, but i can't seem to rearrange it correctly!

Here is the method i used:

v = 1/2π x kf / m
therefore: v/1/2π = kf / m
(v/1/2π)2 = kf / m
(v/1/2π)2 x m = kf

Can someone please pick a hole in my rearranging, because i know the actual rearranged equation and this is not it!

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Show us the actual equation. Your presentation has some ambiguity.

kf / m =? √(kf / m) or =? (kf )/m

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I don't think I understand your question but this is the starting equation...
v = (1/2π) x kf / m

does that make more sense?
in brackets is 1 divided by 2 pi

the square root encompasses the kf and the m

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$v = \frac{1}{{2\pi }}\frac{{\sqrt {{k_f}} }}{m}$
cross multiply
$2\pi mv = \sqrt {{k_f}}$
square both sides
${\left( {2\pi mv} \right)^2} = {k_f}$
can you complete it now?

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....the square root encompasses the kf and the m

$v = \frac{1}{{2\pi }}\frac{{\sqrt {{k_f}} }}{m}$

Shaneo - this is why we asked for clarity, it seems that Studiot might have read your equation one way where I would read it another. Maths is unambiguous - text is not

The equation I know in this situation is this (it is mu not m - ie reduced mass rather than mass)

$v = \frac{1}{2\pi}\sqrt{\frac{k_f}{\mu}}$

We have latex tags (not great implementation admittedly) and you can also upload pictures.

On your rearrangement - my first comment would be "the bottom of the bottom to the top". You are dividing by a fraction - switch the bottom of the divider up to the top. Otherwise I think it looks fine - what do you think it should be?

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• 2 weeks later...

Thanks for the help.

I found out my mistake and I now find it easier to treat the equation in a linear format. i.e. v= 1 ÷ 2 pi . Instead of saying v = 1/2pi.

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Thanks for the help.

I found out my mistake and I now find it easier to treat the equation in a linear format. i.e. v= 1 ÷ 2 pi . Instead of saying v = 1/2pi.

Has this really made it any clearer?

I recommend using brackets as shown by mathematic in post#2.

Then there can be no ambiguity.

But thank you for coming back to us with some feedback.

Don't hesitate to post more questions in future.

Edited by studiot

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