Lab Assignment 10: The Simple Pendulum

Instructor’s Overview

The pendulum is an excellent illustrative example of simple harmonic motion.Walker's Physics has a great anecdote of Galileo's observation of oscillatingchandeliers and his subsequent experiments on the simple pendulum. In thislab, we will replicate Galileo's experiment to gain insight into the physics of thependulum. We'll improve on the accuracy of his results by using a stop watchinstead of our pulses to measure the period of the pendulum!

This activity is not based on an eScience experiment, although we will somematerial from the kit for the experiment. For further background on thependulum, refer to Walker's Physics, Section 13-6.

Lab Instructions

1.2.3.

4.

5.6.7.

8.

Cut a one meter length of fishing line.
Tie six washers onto the end of the fishing line.
Tie the other end of the line to a feature attached to a ceiling such as a

stationary ceiling fan. If this is not available, you can recruit an assistant tohold the line in a very stable fashion.

Measure the distance from the holding point to the center of the washers.This is the effective length of the pendulum. Record this value in the tablebelow.

Move the weights no more than 20 degrees from equilibrium and let go.With a stopwatch, time 10 periods (complete oscillations).
Divide the total time by 10 to get the average period for this pendulum.

Record this value in the table below.
Repeat steps 4-7 for four other lengths. Suggested lengths: 100 cm, 80

cm, 60 cm, 40 cm, 20 cm. It is good experimental practice to randomize yourtrials. For example, you could run in this order: 80 cm, 40 cm, 100 cm, 20cm, 60 cm.

Take detailed notes as you perform the experiment and fill out the sectionsbelow. This document serves as your lab report. Please include detaileddescriptions of your experimental methods and observations.

Date:Student:

Abstract

Introduction

Material and Methods

Results

Data Table

Length(meters)	Average period, T(sec)	Average period squared, T2(sec2)

Plots/Analysis

Create a plot of length (x-axis) versus average period (y-axis). You can use aprogram such as Excel to generate your plot. Make sure to clearly label youraxes and indicate units.

Create a plot of length (x-axis) versus (average period)2 (y-axis). Use Excel toadd a linear trend line. Record the slope of the best fit line.

Recall that the period of an ideal simple pendulum is given by the followingrelation:

Squaring both sides of the equation gives us this relation:

Using the slope of your T2 versus L plot, determine the acceleration due togravity.

Based on your results, please answer the following questions:

1.

2.

3.

4.

How close is your experimentally determined gravitational acceleration to9.81 m/s2? What are potential sources for error in the experiment?

For small angles, does the pendulum's period of oscillation depend on theinitial angular displacement from equilibrium? Explain.

Why is it a good idea to use a relatively heavy mass in this experiment?What would you say to a colleague that wanted to use only one washer as thependulum mass?

Use the relation of the period of an ideal simple pendulum, , to calculatethe ratio of the periods of identical pendulums on the Earth and on Mars.Note: The gravitational acceleration on the surface of Mars is approximately

3.7 m/s2.

Conclusions

References