Find the natural frequencies of small oscillations

[rakso]

TL;DR

Find the natural frequencies of small oscillations

Hi,

Given a mechanic-problem, I've linearised a system of two differential equations, which the origin was Lagrange-equations.

The system looks like this;

$$ 5r \ddot{\theta} + r \ddot{\phi} + 4g \theta = 0´ \\ 3r \ddot{\theta} + 2r \ddot{\phi} + 3g \phi = 0 $$
$$ $$

And I shall find the natural frequencies of small oscillations of Theta and Phi. Are you supposed to solve the equations, then check for where the frequencys diverge?

 

[Orodruin]

Solve for $\ddot\theta$ and $\ddot\phi$. You will then have a linear system on the form
$$
\ddot X = - A X,
$$
where $A$ is a matrix and $X$ a column vector of size 2. What is the relation between that matrix and the natural frequencies?

It is unclear what you mean by "where the frequencies diverge".