The Pendulum

Purpose: (1) to determine the factors that affect the period of a pendulum. (2) To use a pendulum to determine the local value of the acceleration of gravity.

Materials:

3 bobs of differing mass

1 stand

1 meterstick

1 length of string 20cm

1 stopwatch

1 protractor

1 platform balance

Introduction

A simple pendulum consists of a small dense weight or bob suspended by a nearly weightless cord from a point about which if can vibrate freely. The point about which the pendulum swings is called the center of suspension. As the pendulum swings from side A to Side B and back again to A, it makes a complete vibration, or cycle. The time required for a cycle is the period of the pendulum. The number of cycles a pendulum makes per second is its frequency. The displacement of the pendulum is its varying distance from the bob’s resting position C. The arc AC, representing the maximum displacement of the bob from C, is the amplitude of the vibration. The length of a simple pendulum is measured from the center of suspension to the center of gravity of the pendulum bob.

Procedure:

  1. Measure the mass of the bob on the platform balance in kg and record it in a data table for each trial.
  2. Keep the starting amplitude in all trials between five and ten degrees. Record the angle in a data table for each trial.
  3. Measure the time, in seconds, required for 20 cycles of the pendulum bob and record it in a data table for each trial
  4. Compute and record the period in seconds.
  5. Measure the length from the center of suspension to the center of the bob and record the length in meters in the data table for each trial.
  6. Keeping the length constant, replace the bob with one having a different mass. Record the mass in kg, the period in seconds, and the length in meters in the data chart.
  7. Repeat step five two more time using different lengths. Record the periods, in seconds, and the lengths, in meters, in the data table for each trial.

Analysis:

  1. From your calculations, what factors affect the period of the pendulum and which do not affect the pendulums period?
  2. How does your calculation of gravity compared to the gravitational constant?
  3. Discuss some of the relationships discovered in this activity.

Interesting properties

A pendulum has some interesting properties, concerning its frequency (how many times it goes back and forth per second).

Dependent of length

The frequency of the pendulum is dependent on the length (L) of the string or wire. The shorter the wire, the greater the frequency or how fast it goes back and forth.

Independent of amplitude

The frequency is independent of the amplitude (A) of the swing, provided the initial angle (a) is not large. At larger angles, there is a slight change in the frequency.

Independent of mass

Also, the frequency is independent of the mass of the bob. In other words a pendulum with a heavy bob will move at the same rate as one with a lighter weight bob. But this only makes sense, since the acceleration of gravity on a falling object is independent of the mass of the object.