PreCalculus                                                                                     Name:                       

CBL TIC,TOC Lab

 

Pendulum motion has fascinated people for hundreds of years.  Galileo studied pendulum motion by watching a swinging chandelier and timing it with his pulse.  Jean Foucault proved that the earth rotates by using a long pendulum which swung in the same plane and showed that the earth rotated underneath it.  The Foucault Pendulum is now an attraction in many science museums around the country.

 

Pendulum motion for small angles is shown to approximate simple harmonic motion and produces a familiar pattern.  In this experiment, you will use a motion detector to plot the position vs. time graph for a simple pendulum.  You will time the motion to calculate the period, and use a ruler to measure the maximum displacement.  You will then use your data to find an equation that describes the position vs. time graph.

 

YOU NEED:

1 CBL Unit

1 TI-83 Calculator with Unit-to-Unit Link Cable & Program “TICTOC

1 Vernier CBL Motion Detector or Ranger Unit

1 Pendulum Bob (Weighted can or ball)

1 Meter Stick

String

Ring Stand with clamp

 

INSTRUCTIONS TO DETERMINE REGRESSION EQUATION:

1.       Your instructor will tell you where the pendulum is set-up.  All other necessary hardware including the TI-83 calculator will be found there.  It is best to elevate the detector and keep the pendulum high enough so that the motion detector does not detect the table or desk.  Position a meter stick along the table so that the zero point is at the motion detector.  Make sure that you align the pendulum bob and the motion sensor screen.

2.       Before the data collection begins, there are two measurements that need to be made and recorded:

•          Measure the distance between the pendulum and the motion detector in centimeters.  Be sure that the distance is at least 75 cm.  Record your measurement in the Activity Data Table.

•          Determine how far you will pull the pendulum away from its original position.  This distance should not be more than 20 cm. Record the distance in the Activity Data Table.

3.       One cycle of the pendulum consists of the motion for one complete swing back and forth.

4.       Run the program TICTOC on the TI-83 calculator.

5.       Follow the directions on the TI-83 screen to complete the activity.

6.       The resulting distance vs. time plot should be sinusoidal.

7.       If you are dissatisfied with your results, press * * to collect new data.

8.       When you are finished and satisfied with your data for this first trial, link the data lists from the demonstration TI-83 to your calculator so that you will have data from which to calculate your group’s regression equation. Before you go onto the next trial, find and be prepared to explain how you determined  the values for A, B, C, and D in the equation: d = A cos [B(t – C)]+D  where d is distance in centimeters and t is time in seconds.

Note: this equation is in a format different from that found on your calculator’s regression command, so you may find it easier to calculate the equation by using critical points from your graph.

 

INSTRUCTIONS TO ASSIST IN PHYSICAL INTERPRETATIONS:

 

1.       To help you determine the physical interpretations of the values for A, B, C, and D in your equation, you may want to do a few other trials but varying some of the measurements. If you already know the physical interpretations, you may skip these additional trials and begin writing your paper. NOTE: Before you begin additional trials, you may want to restore your original data in lists L3 and L4 since the TIC-TOC program puts new data in L1 and L2.

2.       For trial #2, change the distance from the motion while keeping the same pull back distance. Record your distances in the Activity Data Table. Calculate the regression equation for the new data and observe which value changes.

3.       For trial #3, change the pull back distance while keeping the same distance from the motion detector. Record your distances in the Activity Data Table. Calculate the regression equation for the new data and observe which value changes.

4.       You may do more additional trials to help see which measurements affect which variables.

 

ACTIVITY DATA TABLE:

TRIAL #

PULL-BACK DISTANCE (cm)

DISTANCE FROM MOTION DETECTOR (cm)

A

B

C

D

EQUATION

1

 

 

 

 

 

 

 

2

 

 

 

 

 

 

 

3

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

QUESTIONS:

            In your paper, explain what you did in the experiment, how you did your calculations, and include each of the following.

1.         Find and explain how you determined  the values for A, B, C, and D in the equation for your first trial:

            d = A cos [B(t – C)]+D  where d is distance in centimeters and t is time in seconds.

            --Make sure that:  

            (a) before you write your explanation, your equation models the data with reasonable accuracy.  

            (b) In your explanation, include the information from Activity Data Table and that your explanation is typed.

 

2.         Explain the physical interpretations of the variables A, B, C, and D as they relate to the swinging pendulum and your equation d = A cos [B(t – C)]+D. 

 

3.         Print out your data graph with overlayed regression curve and equation at the top, and also print your window dimensions.

 

SCORING:    Total = 50 points.

1.         Math Correctness -- 10 pts

            Explanation -- 10 pts

           

2.         Printouts from calculator using GraphLink -- 7 pts

            Graph of data with model overlayed and equation viewed at top (use 2 decimal places)

            Screen with window dimensions

 

3.         Physical Interpretations -- 8 pts.

            2 pts. each for phase shift, amplitude, period, and vertical shift

 

5.       Structure/Organization/Spelling/Grammar/Neatness -- 15 pts

 

 

TEACHER NOTES FOR TIC-TOC PENDULUM LAB

 

1.       This lab is designed to determine the cosine function model for a sinusoidal regression of the time v. distance traveled of a pendulum.

2.       To save time, it is advisable to set up the equipment for each group ahead of time with the motion detector facing the wall so as not to pick up any unwanted motion.

3.       Equipment suggestions:

1.       A good pendulum is a small can of vegetables tied to a string taped to the can.

2.       A good, stable support stand is a rod screwed into a rectangular base with a double clamp. This equipment can be gotten from your physics department.

3.       Remind students that alignment in both planes is important: bird’s eye view and side view.

4.       Note that a regression curve from the calculator is a sine function and in a different format. So it is easier to determine the cosine equation from direct measurements of the data curve.

5.       The easiest way to check if the regression equation is correct is to observe if it overlays well with the data on the student’s calculator print-out.

6.       Calculations:

A = amplitude = (ymax – ymin)/2

 

This should be equivalent to the pull-back distance in centimeters from the rest position of the pendulum.

 

C = phase shift = x-value of the first ymax

This is the time lapsed from when the CBL was turned on and when the pendulum was set in motion. If the students were in “in sync”, there should be no phase shift.

 

D = vertical shift = (ymax + ymin)/2

This should be equivalent to the distance from the motion detector to the pendulum at rest.

 

B = 2∏/period             

Since the period = 2∏/B = difference of x-values of two consecutive ymax or ymin values. The period is the amount of time in seconds to traverse one complete swing.