# Finishing the equation...am i slow??

• Sep 26th 2007, 03:05 PM
chrsr345
Finishing the equation...am i slow??
Hey guys, heres another piece of my problem. I have to make this whole equation A equal to B going in that order. Is my algebra terrible or am I missing something?

A) ½M ((√2E /√M)(η))² + ½K ((√2E /√K)(ξ))² = E

B) η² + ξ² = 1

im at (η²)E/M + (ξ ²)E/K = E

There is more info and depth to this problem which im not sure if its necessary. But if what I explain is not possible, ill fill in the details.
Thanks again guys
• Sep 26th 2007, 03:53 PM
topsquark
Quote:

Originally Posted by chrsr345
Hey guys, heres another piece of my problem. I have to make this whole equation A equal to B going in that order.

What? (Wondering)

Just to verify this equation:
Quote:

Originally Posted by chrsr345
A) ½M ((√2E /√M)(η))² + ½K ((√2E /√K)(ξ))² = E

$\displaystyle \frac{1}{2}M \left ( \sqrt{ \frac{2E}{M}} \eta \right ) ^2 + \frac{1}{2}K \left ( \sqrt{ \frac{2E}{K}} \xi \right ) ^2 = E$

Then this equation simplifies to
$\displaystyle \frac{1}{2}M \left ( \frac{2E}{M} \eta ^2 \right ) + \frac{1}{2}K \left (\frac{2E}{K} \xi ^2 \right ) = E$

$\displaystyle E \eta ^2 + E \xi ^2 = E$

$\displaystyle E( \eta ^2 + \xi ^2 ) = E$

Equation B says that $\displaystyle \eta ^2 + \xi ^2 = 1$ so the energy equation reads
$\displaystyle E (1) = E$

$\displaystyle E = E$
which is an identity.

Is that what you are trying to do?

-Dan
• Sep 26th 2007, 04:20 PM
chrsr345
thannks so much Dan you are really good. Well you basically nailed it, but what i need to do is fully convert equation A to equation B. Like start with A, and then when im done, it should look like B.

• Sep 26th 2007, 06:53 PM
chrsr345
thank you Dan, you awesome:) I pretty much just had a simple mistake..as usual
• Sep 27th 2007, 05:06 AM
topsquark
Quote:

Originally Posted by chrsr345
thank you Dan, you awesome:) I pretty much just had a simple mistake..as usual

Don't feel bad. Those are the worst kind to correct on your own. ;)

-Dan