## Simple Pendulum

** Purpose **

To determine the value of the gravitational acceleration by using a simple pendulum.

**Objectives**

- To be able to perform an experiment independently.
- To be able to take measurements, obtain results, and interpret them correctly.
- To be able to estimate the accuracy of experimental results.

**Equipment**

- A small object with a hole such as a bead or nut, and a long string
- A measuring tape (or ruler) and a watch. If you don’t have a watch, you can use your cell phone or a web app such as this Java Applet Stopwatch.
- Scissors, a pencil and a scotch tape

** Theory**

A simple pendulum consists of an object with

negligible size hanging on a string. When the object is deflected from

its equilibrium, it swings (oscillates) back and forth. The time for one

complete cycle (oscillation) is called the period of oscillations, T. For

small angles of deflection, the period of the simple pendulum is

given by the following formula:

Period = 2π √ L ⁄ g ,

where L is the length of the pendulum and g is the gravitational acceleration.

In order to increase the accuracy of the final result, the time must be measured several times. The average of these values will be taken as the time it takes for the pendulum to swing.

** Preliminary Setup**

- Cut approximately 1 meter long string.
- Tie one end of the string to the bead and the other to the pencil.
- Tape the pencil onto a table or any other surface, so that the bead is hanging freely. This is your simple pendulum.

**Activity**

**Determine the value of the gravitational acceleration.**

**Procedure**

Determine the period of the oscillations.

- Measure the length of the string from the pencil end to the bead.
- Pull the bead approximately 5 cm to the side from its equilibrium position and let it go.
- Measure the time for 20 oscillations, t, and write it down
- Repeat the procedure seven times and record your data
- Average the seven values and determine the period of oscillations by dividing the time t by 20.

**Data and Results**

Record your measurements in the following table:

L (m) | t_{1} (s) |
t_{2} (s) |
t_{3} (s) |
t_{4} (s) |
t_{5} (s) |
t_{6} (s) |
t_{7} (s) |
t_{av} (s) |
T_{av} (s) |

**Results**

Using the formula for the period of a simple pendulum, determine the gravitational acceleration, g. Write down the results in the following table:

  L (m)   |   T_{av} (s)   |
  g (m/s^{2})   |

#### Questions

**Question 1.** How accurate is your result. Compare with the value for the gravitational acceleration. To what digit do your results and the established value agree?

**Question 2. ** List all the factors (order them according to their impact) that might have affected the accuracy of your results.

**Question 3. ** Which of the above factors can be removed and which were outside your control?