1. Lesson 4

1.7. Explore 3

Mathematics 30-2 Module 6

Module 6: Sinusoidal Functions

 

Although creating a curve of best fit by hand can be done, it is often easier and more accurate to create a curve by using a graphing calculator or some other graphing technology. You can also use this technology to find the regression equation that best fits the data given. A regression is actually a statistical analysis that assesses the association between two variables. It is very difficult to calculate a regression by hand, so you can use technology to help.

 

Try This 3

 

Hagan is performing an experiment with a spring attached to a weight. She places a distance sensor 50 cm below the weight. She then lifts the weight 10 cm and turns on the distance sensor as she drops the weight.

 

This illustration shows four sequential diagrams. The first diagram shows a hanging spring with a weight attached to the end of the spring above a distance sensor. The distance between the weight and the distance sensor is labelled height equals 50 centimetres. The second diagram shows a hand lifting the weight 10 centimetres. The third diagram shows the weight stretching the spring further than it was originally, and the final diagram shows the spring compressed with the weight up high again.

hand: iStockphoto/Thinkstock

 

Hagan received the following information from the sensor.

 

Time (s)

Height (cm)

0

60.0

0.2

57.7

0.4

53.2

0.6

46.9

0.8

41.9

1.0

40.0

1.2

42.8

1.4

50.9

1.6

56.9

1.8

59.6

2.0

59.4

Time (s)

Height (cm)

2.2

53.2

2.4

46.0

2.6

41.7

2.8

39.8

3.0

43.2

3.2

51.5

3.4

58.1

3.6

59.8

3.8

58.2

4.0

51.4


 

If you are unfamiliar with using your calculator for data entry and/or data regression, you may need to consult the calculator’s manual or contact your teacher for assistance with this activity.

  1. Make a scatter plot of the data using a graphing calculator.
  2.  
    1. Use your calculator to determine a sinusoidal regression equation for the data. Record this equation.
    2. Graph the regression equation on the same grid as your scatter plot. How well does the regression equation match the data?
  3. What is the period of this graph? Explain how you determined the period.
  4.  
    1. Determine the height at 1.34 s.
    2. Determine the height at 200.0 s.
    3. Determine the first three points where the weight is at a height of 55.0 cm.

course folder Save your responses in your course folder.

 

Share 3

 

With a partner or in a group, discuss the following questions based on your graph created in Try This 3.

  1. How did your strategies compare for determining the measures in question 4?
  2. How accurate do you expect your heights from questions 4.a. and 4.b. to be? Explain.

course folder If required, save a record of your discussion in your course folder.