A circular, very heavy ring is placed horizontally. One of its diameters is made of a thin, rigid wire of length $10a$. A drilled ball of mass $4m$ is placed in the middle of this wire, and a spring with a rest length a and stiffness $k$, strung on the wire, is attached to both sides of the central ball. We place two balls of mass $3m$ at the outer end of both springs. These balls are connected to the outer end point of the diameter by a spring of rest length $4a$, but also with stiffness $k$. The outer end of these springs is fixed to the end points of the diameter. The balls can move freely along the wire without friction, but are always connected by the springs. The system is rotated with an angular velocity $\Omega$ around an axis perpendicular to the plane of the ring. The effect of the motion of the balls on the rotation of the ring can be neglected.
Hint: it is advisable to introduce the fundamental frequency $\omega_0 = \sqrt{k/m}$ and the dimensionless parameter $p = 12 \Omega^2/\omega_0^2$, and to answer the following to questions in those terms.
Let’s examine the stability of the stationary positions as a function of the parameter $p$.
Let the value of the parameter $p$ now be $p = 23/12$. In the time period $t < 0$, the system rotates with an angular velocity $\Omega$, and the balls oscillate with the lowest frequency. At time $t = 0$, the vibration is just at the zero displacement relative to the stationary positions. At this moment, the movement of the middle ball is momentarily stopped, and then the ball is released.