LabAssignment 10:  The Simple Pendulum

Instructor’s Overview

The pendulum is an excellent illustrativeexample of simple harmonic motion. Walker’s Physics has a greatanecdote of Galileo’s observation of oscillating chandeliers and his subsequentexperiments on the simple pendulum.  Inthis lab, we will replicate Galileo’s experiment to gain insight into thephysics of the pendulum.  We’ll improve onthe accuracy of his results by using a stop watch instead of our pulses to measurethe period of the pendulum!

This activity is not based on an eScienceexperiment, although we will some material from the kit for theexperiment.  For further background onthe pendulum, refer to Walker’s Physics,Section 13-6.

Lab Instructions

1.  ¨ Cut a one meter length of fishing line.

2.  ¨ Tie six washers onto the end of the fishing line.

3.  ¨ Tie the other end of the line to a feature attachedto a ceiling such as a stationary ceiling fan. If this is not available, you can recruit an assistant to hold the linein a very stable fashion.

4.  ¨ Measure the distance from the holding point to thecenter of the washers.  This is theeffective length of the pendulum.  Recordthis value in the table below.

5.  ¨ Move the weights no more than 20 degrees fromequilibrium and let go.

6.  ¨ With a stopwatch, time 10 periods (completeoscillations).

7.  ¨ Divide the total time by 10 to get the average periodfor this pendulum.  Record this value inthe table below.

8.  ¨ Repeat steps 4-7 for four other lengths.  Suggested lengths: 100 cm, 80 cm, 60 cm, 40cm, 20 cm.  It is good experimentalpractice to randomize your trials.  Forexample, you could run in this order: 80 cm, 40 cm, 100 cm, 20 cm, 60 cm.

Take detailednotes as you perform the experiment and fill out the sections below.  This document serves as your lab report.  Please include detailed descriptions of yourexperimental methods and observations.

Date:

Student:

Abstract

Background

Objective

Hypothesis

Introduction

Material and Methods

Results

Data Table

Length (meters)

Average period, T (sec)

Average period squared, T2 (sec2)

Plots/Analysis

Create a plotof length (x-axis) versus average period (y-axis).  You can use a program such as Excel togenerate your plot.  Make sure to clearlylabel your axes and indicate units.

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

Recall thatthe period of an ideal simple pendulum is given by the following relation:

Squaring bothsides of the equation gives us this relation:

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

Based on yourresults, please answer the following questions:

1. How close is your experimentally determined gravitationalacceleration to 9.81 m/s2? What are potential sources for error in the experiment?

2. For small angles, does the pendulum’s period of oscillation dependon the initial angular displacement from equilibrium?  Explain.

3. Why is it a good idea to use a relatively heavy mass in thisexperiment?  What would you say to acolleague that wanted to use only one washer as the pendulum mass?

4. Usethe relation of the period of an ideal simple pendulum,  , to calculate theratio 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