Accelerated Pre-Calculus LabName ______
Slinky Period ______Date ______
Objective: Model the motion of the ”Slinky” using the CBR.
Equipment: CBR“Slinky”
CalculatorRuler
TapeBooks
DeskIndex Card
1. Draw your setup below.
- Run EasyData, then from the main menu chose Setup, then TimeGraph. Change your time to about 5 seconds. (If this doesn’t give you a good graph, adjust this number until you get a graph you like.) Set the “Slinky” in motion and start collecting data. Repeat this process until you get a satisfactory graph.
3. Paste or sketch this graph below.
4. Using the "Trace" feature, locate four points that would help you write the
equation of this curve and label them on the above sketch.
5. Why did you choose these four points?
6. If you could only have chosen two points, what two would you have chosen and why?
7. Use the information from these four points and show work to determine:
A)The period of your graph.
B)The amplitude of your graph.
C)The phase shift of your graph if you call it a cosine curve.
D)The vertical shift of your graph.
8. Write an equation for your graph using the information from problem #7.
9. Graph this equation on the same data plot. Does it appear to be correct?
10. The "Sinreg" feature gives a sine equation instead of one in terms of a cosine function. How should you change your equation in order to call it a sine curve instead of a cosine curve? Do that and write the new equation below.
11. Graph your new equation from problem #10 on the same data plot. Does your new equation any better and/or worse than your old equation from problem #8? Please explain your conclusion.
12. Use the "Sinreg" feature of your calculator to find the best-fit equation of your data. Write the result below.
13. Compare your four "transformation values" from problems #7 and #10 with those found by the calculator. Which values were the closest? Which ones were the farthest away?
14. Look at the “Slinky” data and compare it with your prediction equation. Although the equation should provide a fairly decent fit, there may not be a perfect fit. Explain why this is the case.
One of the reasons you could have listed above could be due to "damping" or the slowing down of the “Slinky” due to friction. The amplitude actually decreases as time increases. Let's use this information to produce a more accurate prediction equation.
15. Transform your equation from problem #8 by removing the vertical shift and write the new equation below. What effect did this have on your graph?
16. Transform your data by subtracting the vertical shift from all your “y” data points and saving the transformed points in L6. Now graph L1 vs. L6 to see your graph centered about the x-axis. Your transformed equation should now fit your new data points.
17. Using the "Trace" feature, locate all of your relative maximum points of the transformed data. Sketch and label them below. You may cut and paste if you like.
18. What type of function do these points model? ______Does this make sense? Explain completely.
19. Show all work to write an equation that models these points.
20. Use this new function as your new amplitude and write this new equation below. Does is appear to fit your transformed data points better?
21. Return the vertical shift to both your equation and the data. Write your new equation below.
22. Graph your new equation from problem #21 on the scatter plot of your original data. Does this equation seem to fit your data better than your original equation did?______Explain completely.
23. Does this new equation from problem #20 seem to fit your data better than the
"Sinreg" equation produced by the calculator did?______Explain completely.
24. Use the TI-Connect to print your data with your dampened curve (the equation from problem #21), and attach it to your lab. Be sure to label your graph well!