# Theory of small oscilations

1. Apr 21, 2014

### rmfw

1. The problem statement, all variables and given/known data

(see pic)

$\frac{l_{2}}{l_{1}} = \frac{1}{4}$
$\frac{g}{l_{1}} = 1$

I need to find the normal modes of oscillation. (for small oscillations)

3. The attempt at a solution

I solved the problem using the matricial way and got the following matrix: (I simplified it using the above ratios)

$V - wT = m \begin{pmatrix} 1 - w^2 & -1/4 \\ -1/4 & 1/8 - w^2/48 \end{pmatrix}$

Solving the determinant of the matrix I got two positive solutions. Now the thing is for each solution I got two different configurations of amplitudes. I thought that each normal frequency would give me only one configuration of amplitudes. Can you make this clear for me? Thanks.

#### Attached Files:

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2. Apr 23, 2014

### BruceW

Hi, sorry but what was the problem statement? where is the mass located? It is hard to follow along without knowing that...