A small particle having a mass m is placed inside the semicircular tube. The particle is placed

Question:

A small particle having a mass m is placed inside the semicircular tube. The particle is placed at the position shown and released. Apply the principle of angular momentum about point O (ΣM₀ = H₀), and show that the motion of the particle is governed by the differential equation θ'' + (g / R) sin θ = 0.