Rearranging equations with square roots...

[shaneo]

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


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

[mathematic]

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

√k_f / m =? √(k_f / m) or =? (√k_f )/m

[shaneo]

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

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

the square root encompasses the kf and the m

[studiot]

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

[imatfaal]

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

 

 

[math]v = \frac{1}{{2\pi }}\frac{{\sqrt {{k_f}} }}{m}[/math]

 

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)

 

[math]v = \frac{1}{2\pi}\sqrt{\frac{k_f}{\mu}}[/math]

 

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?

[shaneo]

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.

[studiot]

 

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 May 26, 2014 by studiot