Inserted mass on a rotating ring, problem with solution interpretation

[albandres]

Homework Statement

Its about a system like in picture. I have it solved alredy BUT I still have a problem
After getting the dynamic equation by Newtonian and Lagrangian methods I solved one of them making the hipótesis of Little oscillations. This diferential equation has three solutions depending on ω.

http://www.acienciasgalilei.com/public/forobb/galeria/tmp4/a44be89a0d.png

Homework Equations

The problem is that one of them is: θ=θocosh(Ωt) but when we increase t, θ grows exponetially till the infinite! How can this be posible if this is a solution only suitable for small oscillations?

Thanks!

PD: sorry about my english (Im spanish, and I am very tired now)

 

[tiny-tim]

ola albandres! welcome to pf!

Its about a system like in picture.
…
The problem is that one of them is: θ=θocosh(Ωt) but when we increase t, θ grows exponetially till the infinite! How can this be posible if this is a solution only suitable for small oscillations?

erm …

no picture! ​

it's difficult to say without knowing the set-up, but does this solution represent an unstable equilibrium?