SETUP

1. Using a meter stick, measure the length of the Pendulum Bar (ignore the small tabs on the ends) and the distance between holes.
2. Put the Rotary Motion Sensor on the rod stand and plug it into the Universal Interface 850. See Figure 3.
3. Use the mounting screw to attach the Pendulum Bar to the Rotary Motion Sensor using the hole that is the end of the rod

 Figure 3: Experimental setup for the physical pendulum and Universal Interface 850.

PROCEDURE

1.   Open PASCO Capstone on the desktop. Select “Sensor Data” and create a graph of angle versus time by clicking on the y-axis label and then selecting “Angle (rad)”. The x-axis should be labeled “Time (s)” already.

2.   Displace the pendulum less than 15o (0.35 rad) from equilibrium, then click on the red Record button to the bottom left of your Capstone graph. Release the pendulum and make sure Capstone is collecting the data.

3.   Click STOP after about 15 oscillations. Perform analysis described below before deleting this run.

4.   Move the mounting screw to the next hole down from the end. Press ‘Delete Last Run’ in the bottom of Capstone. Repeat steps 2 and 3 until hole 7 is reached.

ANALYSIS

1.   Find the period of oscillation for each position of the pivot.

a.   Select Run #1 on the graph.

b.   Double click at the point on the first peak of Angular Position. Click on the left button “Add coordinates.” With the left-right arrows on the keyboard, move to the nearest points to find the maximum. You may have to click on the position again for the left-right arrows to work. Read the value of time.

c.   Count 10 periods to the right and repeat the previous procedure. Determine the time for one period by measuring the time for 10 periods and divide by 10. Record your values for time and period in the table in the Results section, and in the Excel sheet. Do not forget to include uncertainty (see Question 8).

d.   Go to step 4 of procedure.

2.   The Physical Pendulum excel sheet will plot a ‘Period’ vs. ‘Distance from Center of Mass’ graph. Determine which distance gives the minimum period of oscillation of the pendulum bar. Copy your table into the Results, Part 2 section of your report.

Question 9.

It can be shown using calculus that the minimum period for this pendulum occurs when or , where   is the center of mass for the physical pendulum. Does your data and graph agree with the analytic value for the location of the minimum period for this pendulum? Record and compare these two values. Provide some sources of error as to why they might not agree.