1. PSC 151 Laboratory Activity 4 Graphical Analysis IIB Nonlinear Graphs 2 and The Motion of a Simple Pendulum

2. Using Graphical Analysis to Investigate the Motion of a Simple Pendulum

3. The composition and motion of a pendulum can be described in terms of four measurable quantities. Independent Variables Mass Length Amplitude Dependent Variable Period On which of the independent variables is the period dependent? Only two variables can be investigated at a time. Period versus Mass Length & Amplitude constant Period versus Amplitude Length & Mass constant Period versus Length Mass & Amplitude constant

4. Investigating the dependence of the Period on the Mass of the pendulum. Varying the mass while keeping the amplitude and length constant

5. Experimental Set-Up As the pendulum swings the CBR emits sound waves which reflect off of the pendulum and return to the CBR. The CBR calculates the distance to the pendulum and sends the data to the TI-83 which then plots the position of the pendulum versus time.

6. CBR / TI-83 Set-UP Connect the CBR to the TI-83 Press: APPS Press “4”CBL/CBR Press “Enter” Press “2” Data Logger

7. Data Logger Set-Up Press: Enter

8. CBR/CBL Set-Up continued Press “2”CBR After CBR-CBL link has been tested: Press: “Enter” After “Status OK”: Press: “Enter” When you are ready to begin taking data” Press: “Enter” After data collection is complete the TI-83 will plot a graph of the pendulum’s position versus time.

10. Taking Data From the Graph: Determining the Period

11. Trial 1 Trial 2 Measuring the Period

12. Dependence of the Period on the Mass of the Pendulum Each group will use a different mass and determine the pendulum’s period. Then the period related to each mass will be recorded in a composite data table. From this composite data table each group will determine whether or not the period of a pendulum depends on its mass.

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14. Dependence of the Period on the Amplitude and Length of the Pendulum

15. We will now use Interactive Physics to simulate the motion of a simple pendulum and determine the dependence of the Period on Amplitude and Length. Does the Period of a Pendulum depend on its Amplitude? We will first exam the dependence on the Amplitude by choosing a mass (6kg) and a length (10m) and holding them constant while varying the amplitude.

16. Does the Period depend on the Length? Choose a mass (6kg) and amplitude (10m) and hold them constant while varying the length.

17. Does the Period of a Pendulum depend on its Length? What is the mathematical relationship between Period and Length?

18. We will begin by plotting a graph of Period, T versus Length, L. If this graph is a straight line we then determine its slope and y-intercept and use the general slope-intercept equation to determine the relationship between T and L.

19. If the graph of period versus length is not a straight line we must determine what function of L to graph next. Study the various graph shapes to determine which one most resembles the graph of Period versus Length. Once a new function of L has been chosen, create a new column in the data table for that function.

20. Revised Data Table Convert lengths based on new function.

21. If this graph is a straight line determine is slope and intercept, and use the general slope-intercept equation to determine the relationship. If this graph is not a straight line, continue the process with a different function of L until a straight line graph is achieved.