Simple Pendulum Purpose 1. To study the simple pendulum and how the period time, relate to the Length, of the simple pendulum. 2. To find the value of , the acceleration of gravity near the earth surface, based on the relation between the period, and the length, of the simple pendulum. Introduction A simple harmonic motion is a motion where the net force, on an object, called the simple harmonic oscillator, has a magnitude that is proportional to the displacement from some equilibrium position, and a direction that always points towards the equilibrium position and is therefore known as a "restoring" force: where c is a constant. For simplifying the notation we will write simply as , where it is understood that is the displacement from some equilibrium position. Displacement and acceleration of a simple harmonic oscillator are related by the equation: This last equation is equivalent to the statement of SHM in Eq. (1), since force and acceleration are related by Newton's 2nd Law. is called the angular speed of the motion. For simple harmonic motion is constant and is given by: where is the time of one complete oscillation - for example, a simple pendulum is as shown