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 (MO = H # O), and show that the motion of the particle is governed by the differential equation u $ + (g>R) sin u = 0.

STA3032 Week 3 2.5.10 COMMON CONTINUOUS DISTRIBUTIONS 1 A uniform random variable places equal weight to all values within its support and is continuous. a A uniform random variable has p.d.f. 1 f x = b−a for a≤x≤b 2 Normal a The normal distribution has parameter µ and a scale parameter σ2 b Normal distribution has p.d.f. −1(x−μ) 1 2σ f(x)= e for -∞