Need help re-arranging an equation!

Hey all I need some help re-arranging this equation so I can find z here it is:

also is w^2/wn^2 the same as (w/wn)^2? so I could replace w^2/wn^2 with say r^2?

x= (w^2/wn^2) / (sqrt( {1-w^2/wn^2}^2 + {2***z***w/wn}^2))

So I have the value for x and I need to find the value of z. I have had a couple of goes at it and I am honestly not sure if what I am doing is right or not.

Thanks for any and all assistance in advance!

Re: Need help re-arranging an equation!

$\displaystyle \frac{w^2}{(wn)^2} = \frac{w}{wn} \cdot \frac{w}{wn} = \left(\frac{w}{wn}\right)^2$, if that helps you to simplify. You can probably see it can be further simplified.

Re: Need help re-arranging an equation!

Awesome I thought so! :) Thanks rowe, where do I go first? Do I get rid of the square root or can I take the entire bottom half of the equation over and times by x ?

$\displaystyle x={r^2}/{sqrt( (1-r^2)^2 + (2*z*r)^2)}$

Re: Need help re-arranging an equation!

will the sqrt just cancel out the squares on the brackets?

Re: Need help re-arranging an equation!

crap= given wrong equation to start with- real one is here:

$\displaystyle x= (M*R/m)*(r^2) / (sqrt( {1-r^2}^2 + {2*z*r}^2))$

Re: Need help re-arranging an equation!

So your equation is, $\displaystyle x = \frac{M\cdot\frac{R}{m}\cdot r^2}{\sqrt{{(1-r^2)}^2+2zr^2}}$, and you need to solve for $\displaystyle z$?

Re: Need help re-arranging an equation!

oh, poo, the M*R/m was just set next to the other equation no multiplication sign but a gap between the horizontal divide line if that makes sense? I am sorry

Re: Need help re-arranging an equation!

No worries; did you mean:

$\displaystyle x = M\cdot\frac{R}{m}\cdot\frac{r^2}{\sqrt{{(1-r^2)}^2+2zr^2}}$ ?

You can actually hover over any equation to see the TeX being used. It takes a bit of learning to write what you want but it definitely speeds things up once you know how to write stuff properly.

Re: Need help re-arranging an equation!

If that is the same as $\displaystyle (M*R)/m$ then thats the one! I'm sorry! Slowly learning this Latex thingimy.:) Oh, and the 2*z*r was in brackets then squared so : $\displaystyle (2*z*r)^2$

I hope that works!

Re: Need help re-arranging an equation!

Sorry rowe, thanks for your patience with me! :)

Re: Need help re-arranging an equation!

Cool, so we have:

$\displaystyle x = \frac{MR}{m}\cdot\frac{r^2}{\sqrt{{(1-r^2)}^2+{(2zr)}^2}}$ and we need to solve for $\displaystyle z$. The first step is to remove the square root from the denominator. Do you know how to do this?

Re: Need help re-arranging an equation!

I am not sure, no sorry, I thought that the squares on the brackets underneath the sqrt would cancel?

Re: Need help re-arranging an equation!

Re: Need help re-arranging an equation!

Quote:

Originally Posted by

**Rhys101** I am not sure, no sorry, I thought that the squares on the brackets underneath the sqrt would cancel?

No. There are two terms under the radical, and we cannot split a radical over addition. So

$\displaystyle \sqrt{a^2} = |a|$

but it is not generally true that

$\displaystyle {\color{red}\sqrt{a^2 + b^2} = |a| + |b|}\quad\leftarrow$** Don't do this**.

To get rid of the square root, you'll need to square both sides of the equation.

Re: Need help re-arranging an equation!

Ok cool so do I need to flip the equation to square everything? so I get $\displaystyle (1/x)^2$? and $\displaystyle (m/MR)^2$? DO I need to square the r^2 on the bottom as well, If I have flipped the equation?