1. ## expansion of equation

Does anybody understand how it goes from (d) to (e)?

2. ## Re: expansion of equation

$(-\omega^2m+2k)(-\omega^2 \cdot 3m +k) - (-k)(-k) = 0$

$(3\omega^4 m^2 - 7\omega^2 mk + 2k^2) - k^2 = 0$

$(3m^2)\omega^4 - (7mk)\omega^2 + k^2 = 0$

note the final equation should have $(3m^2)$ as a factor in the first term instead of $(3m)$...

3. ## Re: expansion of equation

$(-\ w^2m + 2k)(-\ w^23m + k) - (-\ k)(-\ k) = -\ mw^2(-\ 3mw^2 + k) + 2k(-\ 3mw^2 + k) - k^2 =$

$3m^2w^4 - kmw^2 - 6kmw^2 + 2k^2 - k^2 = 3m^2w^4 - 7kmw^2 + k^2.$

It doesn't.