# PENDULUM SHM - Calculator

### PURPOSE

The purpose of this lab is to investigate the special motion we call Simple Harmonic, using a TI graphing calculator and motion detector. You will determine how closely the actual motion follows the theoretical equation for SHM.

### MATERIALS

 TI Graphing Calculator Interface (LabPro or CBL2) Motion Detector Link Cable Ring Stand Pendulum Clamp Pendulum Bob (sphere preferred) String Meter Stick

### SETUP

1. The Motion Sensor needs to be a minimum distance away from the pendulum bob when it is hanging straight down -- 50 cm if the Motion Detector is blue, or 20 cm if the detector is green or black. The area between the sensor and the pendulum should be kept free of extraneous items that could cause unwanted reflections.

2. Make sure the sensor is pointed directly at the pendulum bob, and have the pendulum level with the sensor.

3. The swing of the pendulum should be relatively short, moving no more than about 5 cm.

4. Measure the length of the pendulum, measuring from the bottom of the support to the centre of the pendulum bob.

### PROCEDURE

1. Set up the equipment as shown and described above. The Link Cable should be connected between the interface and the calculator. The Motion Detector should be plugged into the port labeled "DIG/SONIC".

2. Turn the calculator on. You will use one of two programs, either Datamate or Easy Data. Follow the section below for the program you are using.

3. Datamate -- Select Datamate by pressing [APPS] then scrolling down to the program. Click [ENTER] to launch.

4. The default data collection with the Motion Detector is for 5 seconds. Unless your pendulum is very long or very short, this will prove adequate for this lab. You do not have to do anything with SETUP.

5. With the pendulum moving freely, press [2] to START data collection. The screen should indicate "SAMPLING" while the Motion Detector emits a series of clicks.

6. At the end of collection, data will be exchanged between the interface and the calculator then you will be presented with graph of position (distance) versus time. Does the graph resemble what you would draw yourself if you were sketching the motion?

7. Go to step12.

8. EasyData -- Select EasyData by pressing [APPS] then scrolling down to the program. Click [ENTER] to launch.

9. The default data collection with the Motion Detector is for 5 seconds. Unless your pendulum is very long or very short, this will prove adequate for this lab. You do not have to do anything with SETUP.

10. With the pendulum moving freely, press the button that's immedicately below the menu choice at the bottom of the screen, START. The screen should indicate "SAMPLING" and show a series of dots near the bottomwhile the Motion Detector emits a series of clicks.

11. At the end of collection, data will be exchanged between the interface and the calculator then you will be presented with graph of position (distance) versus time. Does the graph resemble what you would draw yourself if you were sketching the motion?

12. Measuring -- When the graph is displayed, tracing has already been turned on. Use the left- and right-arrows to move back and forth across the graph. At each point you will be given the time (X) and the position (Y). Get data from the graph to determine and record the following items:

1. The period, T _______________

2. The amplitude, A _______________

3. The midpoint of the swing, m _______________

13. From your data, write the equation which describes the motion, as per the equation presented in class:
y = m + (A * sin (2 p t / T)) =

Note that you need to add a term m, the midpoint of the swing, so that the graph you draw matches the motion.

14. Datamate -- Press [ENTER] twice to get back to the menu. Choose "QUIT". Note the lists that are used for the data, with L6 being the default for position data.

15. EasyData -- Press the button for MAIN, then choose QUIT. Note the lists that are used for the data with L6 being the default for position data.

16. Press [Y=] and enter your equation as Y1 = . Go to [STAT PLOT] to turn on the graph of L1 vs L6, the Distance vs Time. Press [GRAPH] then [ZOOM]-[9]. Compare your theoretical graph (solid line) with your data. If needed, make adjustments to the equation until it matches the graph as well as you can get it. When finished, enter your final equation.
Final Equation:

17. Now use your final equation to derive an equation for the velocity vs time of your pendulum. Write it here:
v(t) =
18. Enter your equation for velocity into Y1 = . Use [STAT PLOT] to set up the graph of L1 vs L7, the Velocity vs Time graph. Press [GRAPH], then [ZOOM]-[9]. How well does your theoretical equation match the data. Make any adjustments to match the two up as well as possible, then write your final equation here:

Final Equation:

Explain any differences between the original equation and your final equation for the velocity.

### Some of the Various Configurations Possible:

 Calculator Interface Program TI-84+ Direct Connect (Go! Motion or CBR2) EasyData TI-84+ LabPro or CBL2 EasyData TI-83+ Silver Edition Direct Connect to Go! Motion EasyData TI-83+ LabPro or CBL2 Datamate TI-83 LabPro or CBL2 Datamate

For information on Datamate, EasyData, LabPro, CBL2, Go! Motion or TI graphing calculators, go to www.vernier.com. In order to run EasyData version 2, you must have the calculator's operating system upgraded to a very recent version.

Written by Clarence Bakken. Updated 2/03/07