Category Archives: M2 mechanics

Answer to STEP III 2007 Q.9

III/2007/9 – Two small beads, A and B, each of mass m, are threaded on a smooth horizontal circular hoop of radius a and centre O. The angle θ is the acute angle determined by 2 θ = AOB.

The beads are connected by a light straight spring. The energy stored in the spring is
mk^2a^2(\theta - \alpha)^2
where k and α are constants satisfying k > 0 and \frac{\pi}{4} < \alpha < \frac{\pi}{2}
The spring is held in compression with θ = β and then released. Find the period of oscillations in the two cases that arise according to the value of θ and state the value of β for which oscillations do not occur. Continue reading