Purpose
To let students become familiar with measuring with LabPros, meter sticks, and triple beam balances, identifying vibrations and to develop critical thinking skills. Secondly, to introduce student to a technique of data analysis using linear regression.
Equipment
Each group needs the following equipment:
 2 meters of string
 1 LabPro attached to a computer station
 1 desktop trapeze
 1 meter stick
 1 triple beam balance
 1 2hole stopper
 1 1hole stopper
 1 200gram mass
Procedure
Students will work in teams of two or three. On each team, one member will manipulate and measure the suspended pendulums, a second member will operate the LabPro, and the third member will record the data provided in the group's data chart.

The team member working with the pendulums must initially measure the length of each pendulum using 10 washers as the "bob". The length of a pendulum is defined as the distance from the pendulum's point of suspension (its pivoting position) to the center of mass of its bob (the mass hanging from its end). Between trials, he/she will change the length of the team's pendulum by lowering the cross beam 1015 centimeters. When releasing the pendulum, make sure that its amplitude is very small, less than 15º, as larger angles may result in inaccurate results.

The team member operating the LabPro must make sure that the motion detector is looking directly at the pendulum's bob (2 stoppers) as it swings. The bob should never get closer than 40 cm from the detector during its oscillations. The motion detector can rest on the table or on the floor. When you are ready to run a trial, first start the LabPro by clicking Collect, then release the pendulum. Run your trial for 10 seconds. Then highlight the region either between the first and last crest or the first and last trough. Record the "dx" which represents the duration of time highlighted and count the number of intervening vibrations.

The team member recording the data should complete the following data charts.
2stopper data

trial number 1

trial number 2

pendulum length (cm)

duration

number of vibrations

duration

number of vibrations




















































Before running the last three trials, we need to record the mass of the two stoppers used as our bob.
mass data

2stoppers (grams)




Now replace the 2stoppers with a 200 gram mass and run three more trials. Let the lengths of these three pendulums be different than those for your original 10 trials.
both stoppers data

trial number 1

trial number 2

pendulum length (cm)

duration

number of vibrations

duration

number of vibrations


















Sample Data
In the following blanks, input the information from your original data tables for the second trial of your 7thlength of the 2stopper bob and the second trial of your 2ndlength of the 200gram bob. Do NOT add units to your answers; the units are supplied for each column.

second trial

length (m) 
duration (sec) 
vibrations 
frequency (hz) 
period (sec) 

Analysis Using all of your data for the 2stopper bob and as well as the 200gram mass, complete the following data chart. Note that there are a total of 13 rows, 10 for the "2stoppers" and 3 for the "200gram mass."
pendulum length (m)

average
period #1

average
period #2

Period
T (sec)

Period^{2}
T^{2} (sec^{2})


































































The team member working with EXCEL is to open this worksheet and input the data from the two green columns in the last chart. Remember that the lengths of your pendulums MUST BE in meters, not centimeters as originally measured.
After you fill in the requested information in column M, save your file in your period folder as
LastnameLastnamePendulum.xls
where each member's last name is included in the file's name. After your EXCEL file has been completed and saved, come to the print station and print a copy of each file for your lab report and for any group member who would like to keep a copy.
Conclusions and Error Analysis:

3. If the accepted value for the gravitational field strength at sea level is 9.8 m/sec^{2}, calculate your experiment's percent error. Show your work on each printout.
The formula to calculate % error is
What is the percent error for your experiment? 
4. State an experimental error, procedural or system, and a correction which would minimize its affects on the outcome of future experiments. Perhaps this physlet animation entitled " The Pendulum" can give you some guidance.
source of error: 
5. In our original data, there were three pendulums that had more massive bobs. We now want to consider whether the mass of the pendulum's bob affected the frequency of the pendulum. Support your answer by comparing or contrasting the data for the more massive bobs. Here are some things you might want to think about when discussing your answer: were the results for these masses outliers or did they merge systematically with the results of the smaller masses? were there relatively similar lengths with different masses that had the same or closely related frequencies? 

Lab Report. When finished, each lab member is to keep their own copy of the EXCEL graph for their notebooks. As a group, you are to turn in one graph in to the oneway box with your calculations for conclusions #1, #2 and #3.