Question

Oscillations and waves!!

Answer 1

Three masses each of mass m/3 arespaced at equal intervals on a massless string of tension T and total length L . Find out the normal mode frequencies .

Answer 2

@irishboy123

Answer 3

See if this helps
http://www.physics.purdue.edu/~jones105/phys42200_Spring2013/Solutions_5_Spring2013.pdf

Answer 4

Great spot. They've generalised the solution which is classy but cumbersome. I think if you go straight for the normal modes, it should simplify as:

\(\vec { \ddot y} = \dfrac{12T}{mL} M \vec y = \alpha M \vec y\), where M is the matrix in the Wolfram screengrab

For trial solution \(\vec y = \vec C e^{i \omega t}\), this means solving \(\alpha M \vec y = -\omega^2 \vec y\)

So Wolfram's eigenvalues fit in as: \(\omega_{1,2,3}^2 = - \alpha \lambda_{1,2,3} \)