Question Description
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 oscillating chandeliers and his subsequent experiments on the simple pendulum. In this lab, we will replicate Galileo's experiment to gain insight into the physics of the pendulum. We'll improve on the accuracy of his results by using a stop watch instead of our pulses to measure the period of the pendulum!
This activity is not based on an eScience experiment, although we will some material from the kit for the experiment. For further background on the 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 attached to a ceiling such as a stationary ceiling fan. If this is not available, you can recruit an assistant to hold the line in a very stable fashion.
4. ¨ 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 table below.
5. ¨ Move the weights no more than 20 degrees from equilibrium and let go.
6. ¨ With a stopwatch, time 10 periods (complete oscillations).
7. ¨ Divide the total time by 10 to get the average period for this pendulum. Record this value in the table below.
8. ¨ 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 your trials. For example, you could run in this order: 80 cm, 40 cm, 100 cm, 20 cm, 60 cm.
Take detailed notes as you perform the experiment and fill out the sections below. This document serves as your lab report. Please include detailed descriptions of your experimental 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, T^{2} (sec^{2}) |
Plots/Analysis
Create a plot of length (x-axis) versus average period (y-axis). You can use a program such as Excel to generate your plot. Make sure to clearly label your axes and indicate units.
Create a plot of 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 that the period of an ideal simple pendulum is given by the following relation:
Squaring both sides of the equation gives us this relation:
Using the slope of your T^{2} versus L plot, determine the acceleration due to gravity.
Based on your results, please answer the following questions:
1. How close is your experimentally determined gravitational acceleration to 9.81 m/s^{2}? What are potential sources for error in the experiment?
2. For small angles, does the pendulum's period of oscillation depend on the initial angular displacement from equilibrium? Explain.
3. 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 the pendulum mass?
4. Use the relation of the period of an ideal simple pendulum, , to calculate the 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/s^{2}.
Conclusions
References
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