- #1

oswaler

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## Homework Statement

consider the free motion of a plane pendulum whose amplitude is not small. Show that the horizontal component of the motion may be represented by the approximate expression ( components through the 3rd order are included)

[tex]\ddot{x}[/tex]+w[tex]^{2}_{0}[/tex] (1+x[tex]^{2}_{0}[/tex]/L[tex]^{2}[/tex])x - Ex[tex]^{3}[/tex]=0

where w[tex]^{2}_{0}[/tex]=g/L , E=3g/(2L[tex]^{3}[/tex]) and L is the length of the suspension.

## Homework Equations

we have a second order non-linear equation: [tex]\ddot{\Theta}[/tex]+w[tex]^{2}_{0}[/tex]sin[tex]^{2}[/tex][tex]\Theta[/tex]=0

## The Attempt at a Solution

I'm pretty stuck on this. It seems that I need to get a function for x in terms of [tex]\Theta[/tex], but I'm not quite sure where to start. I see here that I'm not going to be able to use the small angle approximation sin[tex]\Theta[/tex]=[tex]\Theta[/tex].

Thanks for any help.