# Normal Modes - 2 springs question

1. Jan 24, 2013

### unscientific

1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

When i do the matrix multiplication of the 2x2 and 2x1 matrix, I get 2 conflicting solutions that don't match at all! So which one do i take to find ratio of X and Y?

2. Jan 24, 2013

### TSny

Are you sure they don't match? What 2 conflicting solutions did you get for the ratio X/Y?

3. Jan 27, 2013

### unscientific

Well it's pretty obvious when it is expanded... the top entry gives something like:

(k/m)Y = (1-√5)(K/2m)X

while the bottom entry gives:

(k/m)X = -(1+√5)(K/2m)Y

4. Jan 27, 2013

### vela

Staff Emeritus
Did you notice that $(\sqrt{5}-1)(\sqrt{5}+1)=4$?

5. Jan 28, 2013

### unscientific

Oh I see it now, thank you!