N otes on Chapter 6 A
pp 51 - 53 of your lab book

• A pendulum is a simple device: a mass on a string.
  
• The period of a pendulum is the time it takes for the pendulum to complete one oscillation. In more common terms, the period is the time it takes to return something to its original state; in the case of a pendulum, it is when the mass is at the same position and is going in the same direction as it was before.

Class participation: What variables do you think the period of a pendulum dependent upon?







In this lab, we want to find out what variables affect the period of a pendulum. We will measure the time it takes for one period, altering one variable at a time. If that variable causes the period to change significantly then we will conclude that the period is dependent on that variable.

It is quite difficult to measure a single period of this pendulum, so we will actually count five periods to reduce our error. (I will show you how to do this in class). You will also repeat every measurement five times. You will need to calculate the average, SD, and SDM of every set of five measurements. You will need to do this because you want to know whether or not the average period of a set of data is equal to another set of data. They are equal only if their error bars overlap.

Procedure:

1. First, change the mass, but keep the length and angle constant.
1. Obtain three masses. They are color-coded red, white, blue.
2. Start with the red mass.
   
3. Set the length of the string at 100 cm.
4. Start the pendulum going at an angle of 5 degrees.
5. Use the stopwatch to measure the time it takes for 5 oscillations.
6. Record this value under Time (5 osc.)
7. Repeat steps 3-5 for a total of five trials.
8. Repeat steps 3-7 with the blue mass.
9. Repeat steps 3-7 with the white mass.
   
2. Second, change the angle, but keep the mass and length constant.
1. Choose the blue mass.
2. Set the length at 100 cm.
3. Start the pendulum going at an angle of 2 degrees.
4. Use the stopwatch to measure the time it takes for 5 oscillations.
5. Record this value under Time (5 osc.)
6. Repeat steps 3-5 for a total of five trials.
7. Repeat for 6, 10, 15, 25, 35, 45, and 55 degrees.
8. Make a plot (by hand or by any graphing program) of the period versus angle. (This can be done at home, if you wish.)
   
3. Third, change the length, but keep the angle and mass constant.
1. Choose the blue mass.
2. Set the length at 30 cm.
3. Start the pendulum going at an angle of 5 degrees.
4. Use the stopwatch to measure the time it takes for 5 oscillations.
5. Record this value under Time (5 osc.)
6. Repeat steps 3-5 for a total of five trials.
7. Repeat for 40, 50, 60, 70, 80, 90, and 100 cm.
8. Make a plot of Period ² versus Length. Given the theoretical equation for the period, find the gravitational acceleration g.
   

Data:

Table I: Mass Dependence: =  5 degrees, L = 100 cm, use the SDM Calculator to calculate these numbers. The SDM Calculator will calculate the period column, the T_ave, the SD, and the SDM. Go to http://www2.hawaii.edu/~jmcfatri/Java/SDMCalculator.html

Red Mass Trial Time (5 osc.) (         ) Period (    ) 1 2 3 4 5 Tave= SD = SDM =	Blue Mass Trial Time (5 osc.) (         ) Period (    ) 1 2 3 4 5 Tave= SD = SDM =
White Mass Trial Time (5 osc.) (         ) Period (    ) 1 2 3 4 5 Tave= SD = SDM =

Table II: Angle Dependence

2 deg Trial Time (5 osc.) (         ) Period (    ) 1 2 3 4 5 Tave= SD = SDM =	6 deg Trial Time (5 osc.) (         ) Period (    ) 1 2 3 4 5 Tave= SD = SDM =
10 deg Trial Time (5 osc.) (         ) Period (    ) 1 2 3 4 5 Tave= SD = SDM =	15 deg Trial Time (5 osc.) (         ) Period (    ) 1 2 3 4 5 Tave= SD = SDM =
25 deg Trial Time (5 osc.) (         ) Period (    ) 1 2 3 4 5 Tave= SD = SDM =	35 deg Trial Time (5 osc.) (         ) Period (    ) 1 2 3 4 5 Tave= SD = SDM =
45 deg Trial Time (5 osc.) (         ) Period (    ) 1 2 3 4 5 Tave= SD = SDM =	55 deg Trial Time (5 osc.) (         ) Period (    ) 1 2 3 4 5 Tave= SD = SDM =

Table III: Length Dependence

30 cm Trial Time (5 osc.) (         ) Period (    ) 1 2 3 4 5 Tave= SD = SDM =	40 cm Trial Time (5 osc.) (         ) Period (    ) 1 2 3 4 5 Tave= SD = SDM =
50 cm Trial Time (5 osc.) (         ) Period (    ) 1 2 3 4 5 Tave= SD = SDM =	60 cm Trial Time (5 osc.) (         ) Period (    ) 1 2 3 4 5 Tave= SD = SDM =
70 cm Trial Time (5 osc.) (         ) Period (    ) 1 2 3 4 5 Tave= SD = SDM =	80 cm Trial Time (5 osc.) (         ) Period (    ) 1 2 3 4 5 Tave= SD = SDM =
90 cm Trial Time (5 osc.) (         ) Period (    ) 1 2 3 4 5 Tave= SD = SDM =	100 cm Trial Time (5 osc.) (         ) Period (    ) 1 2 3 4 5 Tave= SD = SDM =

Assignments: Questions assigned:
1. Does this method yield a more accurate value of g than the air track experiment? What is the limiting factor in this experiment?






2. From your experimental data, what happens when you increase the initial angle of the pendulum? What happens when you increase the mass? the length?



3. To verify that the mass has no effect on the period, you have to compare three numbers with uncertainties. Show your three periods graphically to show that their ranges do (or do not) overlap. (Hint: use error bars!)