This question might seems naive, but I'm not a physics student and got puzzled here.
There are three masses placed on the plane and they form the 3 vertices of an equilateral triangle. Every two of them are connected by a spring with spring constant $k$. It's well known that this system has 6 normal modes:
- translation in the x- or y- axis. These two form an 2d irre-rep of $D_3$ but with a zero frequency of $V$
- a pure rotation. This corresponds to the sign rep of $D_3$.
- breathing mode. This is the identity rep of $D_3$.
- pumping mode. (this has two) These two correspond to the 2d irre-rep of $D_3$ but with a non-zero frequency of $V$.
My question arose when I was looking at the rotation mode: How does this mode look like? I was thinking it's like the follows:
There are no restoring forces in the springs: this is easy to see, but how can the masses move along the circle without any forces that holds them? (so they will not get pushed away by the centrifugal forces?)