What affects the Period of a Pendulum

 

Period:  The time it takes (in seconds) for a pendulum to make one complete back-and-forth swing.  The units for period are: # of seconds/1 complete back-and-forth swing.  Period is represented by the letter T.

 

Your Task:

            You and your group are going to determine which of the following three components of a pendulum affect its period.  There may be only one component which affects the period, there may be two, or perhaps all three affect the period.

     Once you have determined which one(s) affect the period, you are also going to determine how they affect the period.

 

     The three components of a pendulum which you will be studying are:

             1)  The mass at the end of the string (called the “bob”) – measured in grams.

 2)  The length of the pendulum (from where it is tied to the MIDDLE of the

       mass) – measured in METERS (remember, rulers measure in centimeters)

 3)  The angle from which the pendulum is let go.  DO NOT pull the pendulum

       up so high that there is slack in the string when it is released.  Only release it

       from a height where it will remain taught throughout its swing. – measured in

       degrees away from a hanging down position.  Hanging down is 0o.  So,

       pulling it all the way horizontal would be 90o. Use a protractor to measure

       the angle.

 

     You and your group need to create at least 3 different lengths of pendulums using at least three different masses and dropping it from at least three different angles.  HINT:  Only change one variable at a time!  Don’t try to change the length when you change the mass (for example).  It is too difficult to determine what’s going on if too many things are changing.

 

 

How to time the period of the pendulum:  READ THIS CAREFULLY!

 

     Let your pendulum make 10 complete back-and-forth swings and divide the number of seconds it took by 10.  Then, let your pendulum make 20 complete swings and divide the number of seconds it took by 20.  (Remember: Period = # of seconds/1 complete back-and-forth swing).  If the two numbers agree, then you have a pretty accurate period for that pendulum.  If they don’t, try again.

 

How to read your Protractor correctly:  READ THIS CAREFULLY!

 

     When the string hangs straight down, that should be 0o.  However, you will notice that your protractor will read 90o (if you hold it so that the straight edge of the protractor is parallel with the ceiling)  Therefore, you must always SUBTRACT the number you read on your protractor from 90o to get the correct reading.  For example:  If you get a 30o angle reading, it is really 60o.

Pre – Lab:

     Your group will break into three sections:

1.  Mass section

2.  Length section

3.  Angle/height section

 

     Decide who is going to be in which section and do the following:

 

Make a data table which will allow you to collect data for your particular section.  It should include at least 3 “trial” boxes for each variable – Three trials for varying the length, three for varying the mass and three for varying the angle/height.  If you are doing the “mass” section (for example) you will want to make a column for length and angle/height too, but those will be a CONSTANT value (NEVER CHANGING).  Your data table should also include a column for Period and Frequency.

 

    When you come to class on Thursday I will expect to see the following

     1.  Three data tables per group (a data table for changing:  mass, length and   

           angle/height)

     2.  Each section of your group getting to work right away to collect data.  You should

          have a plan and work through it so you can make the most efficient use of your

          time.

 

 

Questions I:  Write your answers to the questions on a separate sheet of paper.  Yes, you must copy the question and then write the answer.

 

1.  How many different tests are you going to run if you change each one of the variables three times and take three different measurements of each change you make?

 

2.  Does the mass of the bob affect the period of a pendulum?  Finish this statement:  “As the mass of the bob increases, the period of the pendulum ___________ “

(increases, decreases, stays the same)

 

3. Does the length of the pendulum affect the period of a pendulum?  Finish this statement:  “As the length increases, the period of the pendulum ___________ “

(increases, decreases, stays the same)

 

4. Does the angle from which the pendulum is released affect the period of a pendulum?  Finish this statement:  “As the angle from which the pendulum is released increases, the period of the pendulum ___________ (increases, decreases, stays the same)

 

5.  What is the definition of “period”  (Hint, it’s in the lab).

 

 

What affects the Period of a Pendulum – Follow up/Graphing

 

Graph:

 

     Use Graphical Analysis to make a graph of period vs. length.  Use the Length and Period data below:

 

     Also, use Graphical Analysis to create a third (calculated) column titled: “Period2”.  Graph Period2 vs. length on a NEW graph.  What do you notice about this line?

 

Curve Fit:

     Use the “curve fit” function on the Graphical Analysis program  and make curves to fit both the lines from Period vs. Length and Period2 vs. Length. 

 

Length and Period Data

 

     All Lengths are given in Meters.

 

X-Length   Y-Period

0.5

1.419185

0.75

1.73814

1

2.007031

1.5

2.458101

1.75

2.655052

2

2.83837

2.5

3.173394

2.75

3.328284

3

3.476279

3.5

3.754811

3.75

3.886598

4

4.014061

4.5

4.257555

4.75

4.374222

5

4.487857

 

Questions II:  Please copy the questions and then answer them (or type your answers beneath the questions if you are using your computer to do this write up).

 

1.  Once you have made the linear curve fit of your period2 vs. length graph, what is the slope of the line?

 

2.  Write a mathematical formula for determining the period of a pendulum based on the length of the pendulum.  What I mean by this is that you need to create a formula which includes T and l (where T = period and l = length in meters).  HINT:  Use the slope of the line from your T2 vs. length graph to help you come up with a formula.  HINT #2:  Your answer needs to look like this:

                                  T = ______________  

 (so, the right side of the equation will have a  sign and there will probably be some kind of constant in your answer as well)

 

3.  Try a length (from your data table) in the mathematical formula you just created and see if you get the period you found experimentally.  (Show your work).

 

4.  Choose any two sets of data points from your period2 vs. length graph and determine the slope of the line by using the formula: y2-y1/x2-x1.  Your answer should be pretty darn close to your answer to question #1.  If it isn’t, you should check your work.

 

 

 

What is due for this lab and in what order?

1.   The three data tables. Combined as one but clearly separated into three sections (varying mass section, varying length section and varying the angle/height section)

2.  Answers to the first set of questions (write the question and then answer them).

3.  Graph (which includes three columns of data and two graphs with their curve fit.)

4.  Answers to the second set of questions (write the question and then answer them).

 

What could you possibly be quizzed on?

1.  What is the mathematical relationship between length and period.

2.  If I give you a pendulum with a known period, could you tell me how long it is?

3.  If I give you a pendulum with a known length, could you tell me its period?

4.  Could you find the slope of a line by looking at a y=mx+b equation?

5.  Could you find the slope of the line if I gave you two sets of data points and plugged them into the formula: y2-y1/x2-x1.

6.  Could you tell me what affects the period of a pendulum and what doesn’t and give me examples of how you know this to be true?