Question 3: Simple Pendulum Figure 3 A simple pendulum consists of a mass m attached to a weightless string of length L (see Figure 3 above). The angle that the pendulum makes with the vertical during its swinging motion is given by 0. a) Using small-angle approximation, the equations of motion of the pendulum can be modelled using Ö +20 = 0 ODE Egn (3) where g is the acceleration due to gravity. ) State suitable initial conditions for this model. i) Using the initial conditions you stated in part a), solve the ordinary differential equation above (ODE Egn (3) to find a particular solution for the motion. i) What makes the model above unrealistic?

Question 3: Simple Pendulum Figure 3 A simple pendulum consists of a mass m attached to a weightless string of length L (see Figure 3 above). The angle that the pendulum makes with the vertical during its swinging motion is given by 0. a) Using small-angle approximation, the equations of motion of the pendulum can be modelled using Ö +20 = 0 ODE Egn (3) where g is the acceleration due to gravity. ) State suitable initial conditions for this model. i) Using the initial conditions you stated in part a), solve the ordinary differential equation above (ODE Egn (3) to find a particular solution for the motion. i) What makes the model above unrealistic?