14. You should already be familiar with the mathematical treatment of an ideal pendulum, in which the pendulum bob is modelled as a point mass on the end of a rigid rod of negligible mass. In this problem you will consider the behaviour of more complex types of pendulum. You will be given all the information you need in the sections below. For a general pendulum of any shape and size the period P is given by p= 2*pie*root(I/gM(LCM)) where g is the acceleration due to gravity, M is the total mass of the pendulum, LCM is the effective length of the pendulum, defined as the distance from the pivot to the centre of mass, and I is the moment of inertia around the pivot point. For a point mass m fixed at a distance r from the pivot I = mr^2, while for a uniform rod of mass m and length r attached to the pivot at one end I = 1/3mr^2 . For more complex objects the total moment of inertia can be calculated by adding together values for the component parts. (c) Now consider the case of a real pendulum, with a bob of mass Mb (which you may treat as a point mass) attached to the pivot using a uniform rod of mass Mr and length L, and find the period in this case. Show that the result for a real pendulum reduces to the results for an ideal pendulum and a rod pendulum by taking appropriate limits.