(Solved): QUESTION 3: [25 points] Consider a bead on a circular loop of radius \( R \). The bead has mass \( ...

QUESTION 3: [25 points] Consider a bead on a circular loop of radius \( R \). The bead has mass \( m \) and is subject to the gravity of earth (with acceleration g). The loop does not move in this problem and we neglect all friction forces. The position of the bead is given by the angle \( \theta \). a) [5pts] Identify the equilibrium positions \( \theta \) of the bead and whether the equilibrium positions are stable or unstable. b) [10pts] At an angle \( 0<\theta<\pi \) the bead moves downwards with a speed \( v_{0} \). Identify all the forces that act on the bead. Calculate the magnitude of the forces components in the tangential and radial directions. c) [10pts] Calculate the period of small oscillations around the stable equilibrium.