Physics 41 Lab 2: The Simple Pendulum
In this experiment we will study how the mass of a pendulum bob, and the
length of the string affects the period of the pendulum in SHM.
(1)   2

L
g
We will also use equation (1) to obtain an experimental value of ‘g’, the acceleration due to gravity.
Equipment: Lab Jack, Table clamp, Long Rod, Pendulum clamp, 3 pendulum balls – (wood,
aluminum,& brass), Single pendulum string, Protractor, Lab Pro, Motion detector & cables
Procedure: Open a Word document for your group lab report. You will also make tables in Excel.
Your lab report will need to include a brief abstract. Please label each part and work in order. Answer
any questions asked in the report in the section in which it was asked, making any notes that are
important and answering the questions in each part. Abstract first on title page alone, followed by the
rest in the order of the lab.
Part 1: Effect of Mass Varying the mass of the bob while holding the length and amplitude
constant.
1. Weigh the bobs to get the total mass. Set up your pendulum with the heaviest bob and determine a
fixed angle (use close to 10 degrees.) Measure the length of the string. Use equation (1) to predict
the pendulum’s theoretical period. Enter these values into your data table.
2. Use the motion detector to graph the periodic motion for as many cycles for which the data is
good (at least 10). Do a sinusoidal fit and get the angular frequency from the coefficient of time,
“B” like we did last lab. Calculate the period by dividing 2 pi by B. This is your experimental
value for the period. Put all this into a table. Repeat 2 more times. Average your values and find a
final percent error between theory and average experimental value. Include a sample loggerpro
plot in your report.
3. Repeat for the two other bobs, keeping the string length and amplitude constant. For each bob you
should have: 3 B’s, 3 periods, the average value of those data points and the average deviation, as
well as a % error between the theoretical period for each bob.
4. Plot the mass vs period using the averaged periods for each mass. Label the axes. You may have
to expand the scale of the axes to see a flat line. Try a linear curve fit. What is the slope of
your line? Show the fit and an R-squared value. What can you conclude about the
dependence of the period on mass? Why or why not was the period independent of mass?
Part 2: Effect of Length
1. Set up a pendulum with the bob that gave you the best results in part 1. Keeping the mass and
amplitude constant, measure the period as above for at least 10 different string lengths. Do just one
logger pro fit for each different length. Using equation (1) and the values of your length, calculate
the theoretical period for the pendulum and enter the value into the data table. Calculate the percent
error between the theoretical and experimental values for each length. Average the errors.
2. Graph your data, Period (s) vs Length (degrees), using your average values. Label your graph. You
may have to change the maximum values on the axes. Do a power-fit for the graph. What is the value
of the exponent? What is the value of the coefficient? How do they compare with those of equation
(1)? Calculate percent error between theory and experiment – that is, is the power ½?
3. Find a value of g and an uncertainty from the data you obtained. Compare to the accepted value of
9.80m/s2 using a percent error.
Make sure you have the page layout set to landscape and do a print preview to make sure the
layout is correct before printing! Print out your data sheet and graphs.
Abstract The abstract should answer the following but it should not be numbered! Read all about
abstracts on our class webpage! The abstract is 20% of the score!
1. What was the purpose of the lab? What did you expect about the dependence of period on mass of
the ball and length of string? What did you find? What was the agreement for theory and
experiment for parts 1 and 2 in terms of average percent errors?
2. What experimental value did you obtain for g and its uncertainty? How did you obtain it? How
did it compare to the accepted value?
3. Based on the data and analysis from parts 1 and 2, what can you conclude about the effects of
mass & length on the period of a pendulum?