Experiment 7

PERIODIC MOTION:

OSCILLATIONS

PROCEDURE

 

SETTING UP THE APPARATUS

The basic set-up should have been completed for you prior to lab, but you may need to make a few adjustments before taking data. A schematic of the basic arrangement is illustrated in Figure 7-1. The oscillating mass consists of standard weights on a hanging weight carrier suspended from the end of the spring.

The motion detector "sees" the bottom of the weight carrier and reports this position to the DataLogger unit. Data collected by the DataLogger unit is sent to the serial port of the computer and displayed on the computer screen via the LoggerPro application.

 
1.  Before starting, check to see that the motion detector cable is connected to DIG/SONIC #2 of the DataLogger interface box, and that the unit is turned on.

2.  Open the SHM-Motion link. A graph with labeled axes should appear on your computer screen.

3.  Suspend the spring WITHOUT weights, large end up, from the support hook, and position the motion detector on the floor directly under the spring. Do this by sighting through the spring from above to locate the appropriate position of the detector on the floor.

NOTE: This step needs to be done carefully so that the detector "sees" the weight clearly and without interference from, say, the edge of the table or other possible interference. The motion detector must be shielded in case the mass accidentally falls. Be sure the detector is placed securely under the shield and is facing up.
4.  Attach a mass to the spring. Use 150 grams to start (100 grams added to the 50 gram weight holder) and add additional weights only as needed. If you must, adjust the point of support so that the mass is not closer to the motion detector than about 0.75 meter.

5.  Pull the mass straight down about 10 cm and then release it. Don't push it when you release it; just release it cleanly.

6.  After setting the mass in motion, click Collect in the LoggerPro window to begin data collection. Be sure the detector "sees" the mass over its full range of motion. There should be no flat portions to your graph. If there are reposition the mass to a slightly higher point and begin again. Some sources of error could be the detector "seeing" the bench or the clamp, so try to move it as far away from these items as is feasible.

7.  Adjust the distance scale in the Graph Window so that the data nearly fills the graph. To do this, double click anywhere on the graph to get a dialog box; then, under the Axis Options tab, set the necessary maximum and minimum distance values.

8.  When you are satisfied with your set-up and are ready to take actual data, open the SHM Workbook and fill in the header information. Then move on to the activities below.

 

Activity #1: Making distance and velocity graphs.
The LoggerPro software automatically computes velocity and acceleration from the position information supplied by the DataLogger unit. These data are stored in different files within the program each time a run is completed and also can be displayed graphically on the computer screen.

1.  To display the graphs for distance and velocity, open the Distance-Velocity link.

2.  Pull the mass straight down by about 10 cm and then release it. Don't push it when you release it; just release it cleanly.

3.  After setting the mass in motion, click Collect in the LoggerPro window to begin data collection. Be sure the detector "sees" the mass over its full range of motion. There should be no flat portions on your graph. If there are, reposition the detector and begin again.

4.  Adjust the vertical scale in the Velocity Graph window so that the data nearly fills the graph. To do this, double click anywhere on the graph to get a dialog box; then set the necessary maximum and minimum velocity values.

5.  When you are satisfied with your graphs, COPY and PASTE them into the indicated space on the Worksheet.

 

Activity #2: Properties of Periodic Motion
 
1.  To measure the period and frequency of the motion represented by the graph, select Examine under the ANALYZE menu in the LoggerPro window. A vertical line with a cursor will appear. Drag this line to various points on the curve. Values for the x- and y-coordinates of the graph at the position of the cursor will appear on the bottom of the screen---these are the respective time and distance and the time and velocity coordinates.

2.  Set the vertical line at the left-most peak of the distance graph. Record the time listed below the graph in cell E37 of the Worksheet.

3.  Move the vertical line to the right, counting peaks as you go. Set the vertical line on the right-most peak. Record the time given below the graph in cell E38 of the Worksheet. Also record the number of cycles you counted in cell E39. The total time is the difference between these two time values. The period of the motion is the total time divided by the number of cycles counted; that is, the period is the time for one cycle. The frequency is the number of cycles per second, or the reciprocal of the period.
 

The midpoint of the motion is the point where the mass hangs when it is at rest. This position is the equilibrium position. The amplitude of the motion is the maximum displacement from the equilibrium position in either direction. For simple harmonic motion, the displacement from equilibrium should be the same in either direction.
 
4.  Use the cursor again to determine the closest distance and the farthest distance of the oscillating mass from the detector. Enter these values in cells E45 and E46 of the Worksheet.

The equilibrium position is midway between the closest and the farthest distances. The amplitude is the difference between either the farthest distance and the equilibrium distance, or the closest distance and the equilibrium distance. The spreadsheet will do the calculation and display the result.

 

Activity #3: Determining the spring constant
1.  With 150 grams suspended from the spring (50 grams for the carrier plus 100 grams), use the meter stick to carefully measure the equilibrium position of the mass when it is at rest. To do this, stabilize the mass as best you can and measure the position of its bottom surface on the meter stick.

2.  Transfer your data (in kg and meters) for both mass and position to cells B55 and C55 of the Worksheet.

3.  Add a second 100 g mass (so the total is now 250 grams) and measure the equilibrium position again. Transfer these data to cells B57 and C57 of the Worksheet. Repeat with a third mass of 350 grams, and enter the data in cells B59 and C59.

The spring constant k is equal to:

A plot of F vs. Δx will have a Slope equal to the spring constant.

We'll call the first mass m1, and the other two masses m2 and m3, respectively.

4.  The spreadsheet will automatically find the difference in force and the difference in mass, and perform the appropriate division with each pair of data points. The average value of k is displayed in cell F61.

 

Activity #4: Comparing distance, velocity and acceleration graphs
1.  To obtain a plot of the acceleration, open the Three-Graphs link.

2.  Place a total of 250 grams (150 grams plus 50 gram holder) on the spring.

3.  Start the mass oscillating with amplitude of about 10 cm, and record this motion on the screen. Again, make sure the curve is not "flat-topped".

4.  Change the Time axis to display about three complete cycles, and adjust the Distance, Velocity and Acceleration scales until the graphs nearly fills the axes.

5.  Select the combination graph and use EDIT...COPY from the LoggerPro window, and then EDIT...PASTE on the Worksheet.

6.  Print out the Worksheet and use it to develop your lab report.