# Find the natural frequencies of small oscillations

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## Summary:

Find the natural frequencies of small oscillations

## Main Question or Discussion Point

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?

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Orodruin
Staff Emeritus
Homework Helper
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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".

• vanhees71