# Methods: Use of a simple pendulum

### Measurement of g:OBJECTIVE: To measure the acceleration due to gravity using a simple pendulum.

INTRODUCTION:
Many things in nature wiggle in a periodic fashion. That is, they vibrate. One such example is a simple pendulum. If we suspend a mass at the end of a piece of string, we have a simple pendulum. Here, the to and fro motion represents a periodic motion used in times past to control the motion of grandfather and cuckoo clocks. Such oscillatory motion is called simple harmonic motion. It was Galileo who first observed that the time a pendulum takes to swing back and forth through small distances depends only on the length of the pendulum The time of this to and fro motion, called the period, does not depend on the mass of the pendulum or on the size of the arc through which it swings.
Another factor involved in the period of motion is, the acceleration due to gravity (g), which on the earth is 9.8 m/s2. It follows then that a long pendulum has a greater period than a shorter pendulum.

 With the assumption of small angles, the frequency and period of the pendulum are independent of the initial angular displacement amplitude. All simple pendulums should have the same period regardless of their initial angle (and regardless of their masses). The period T for a simple pendulum does not depend on the mass or the initial angular displacement, but depends only on the length L of the string and the value of the gravitational field strength g, according to:

The period T of a simple pendulum (measured in seconds) is given by the formula:

PROCEDURE:

using equation (1) to solve for “g”, L is the length of the pendulum (measured in meters) and g is the acceleration due to gravity (measured in meters/sec2). Now with a bit of algebraic rearranging, we may solve Eq. (1) for the acceleration due to gravity g.

1. Measure the length of the pendulum to the middle of the pendulum bob. Record the length of the pendulum in the table below.
2. With the help of a lab partner, set the pendulum in motion until it completes 30 (25 or 50) to and fro oscillations, taking care to record this time. Then the period T for one oscillation is just the number recorded divided by 30 using (eq. 2).
3. You will make a total of eight measurements for g using two different masses at four different values for the length L.
Note: π = 3.14, 4 π² = 39.44