Question

Consider three particles with masses

m1=m

,

m= 2m

and

m3= 3m

connected

by springs with force constants

k1= 2k

k2= 3k

and

k3= 6k

These particles can move on a

circle of radius

R

(no gravity forces here, restoring forces come from springs only!), see Fig. 2 for

the illustration. Find eigenfrequencies

ω

of small oscillations in this system.

Answer 1

Solution:

Now,

where

Then: =

Determinant is:

so, eigen frequencies: