Thompkins: AP Physics
Simple Harmonic Motion: Pendulum and Mass on a Spring
Introduction
A pendulum consists of a "bob" attached to a string that is fastened such that the pendulum
assembly can swing or oscillate in a plane. For an ideal pendulum, all the mass is considered to be
concentrated at a point in the center of the bob.
Some of the parameters of a simple pendulum include the length (L), the mass of the bob (m),
the angular displacement θ through which the pendulum swings, and the period T of the pendulum,
which is the time it takes the pendulum to swing through one complete oscillation.
When the angular displacement is minimal (θ < 150) the period of a pendulum can be
determined with the
following equation.
T =2
Equipment:
string, pendulum,
stopwatch, meter stick
L
g
Methods
(Note:
significant figures are extremely important in this lab.)
1. Obtain a pendulum setup consisting of a bob, string, and clamp, then secure the string onto the
pendulum clamp. Place the clamp in a position that is firmly held, avoiding any motion as the
pendulum swings to and fro.
2. Accurately determine the length of the pendulum's string.
3. With the stopwatch, determine the period of the pendulum as accurately as possible, generally
Measure the period of the pendulum by counting the time it takes to swing 10 swings and
then divide by 10 to measure the period of one swing (this increases accuracy)
4. Repeat Steps 1 - 3 for four other lengths of pendula with at least 10 cm difference in length.
5. Using the correct equation calculate the acceleration of gravity
Form a data table to organize your data showing all variables, manipulated variables and units.
Analysis
1. Using Excel, plot a graph of L vs T. Then use graphical analysis methods (make a second
graph) to determine the best line fit and perform a regression analysis to determine the slope
of the line.
(Note: Show both graphs in your lab report)
2. Determine a formula for “g” based on the slope of your 2nd graph. Please show all work.
3. Calculate “g”.
4. Find the percent error of your calculated value and the experimental value.
5. Suggest sources of error in this lab.
6. If the mass of the pendulum was changed and the length was constant then what could be
stated about the relationship between period and mass.
7. Predict and discuss the results of this lab on the moon. (Please explain in detail).
Part 2
Procedure:
1) You will be given a spring.
a. The first part of the experiment will be to find the spring constant.
i. Using various masses to collect at least 5 data points.
ii. Show and explain how you determined the spring constant and organize all
data, tables and graphs with the correct units.
iii. Calculate the elastic potential energy using your graph. Explain how you
determined this value.
2) Once you have determined the spring constant, you will now measure the frequency of
oscillation for your system.
a. In this part you will find the time per oscillation for various masses that will hang
from the spring. Time 20 Oscillations.
b. Use the formulas from the first page to develop your experiment.
c.
Please show all work including data tables, graphs and a qualitative/quantitative
description of how you determined the spring constant graphically.
d. Determine your % error for the spring constant.
Conclusion:
Explain what you determined/concluded from each experiment.