Gamma, g, represents the decay function of this damped oscillation. Tomorrow, during our analysis, we will first graph the spring's amplitude vs time and then examine a second graph of the natural logarithm of its amplitude vs time. The slope of LN(y) vs t is negative gamma. Using this slope we will determine the half-life of the spring's decay and verify its value with the data collected from the PSL distance probe today.

A typical graph of this type of oscillation would look like the following sample.

Procedure (set-up):

One member of the group should go to the computer, open PSL and SELECT the experiment entitled First Steps. Now go to RESET PARAMETERS and change the Duration to 20 seconds. Remain in RESET PARAMETERS and change the Number Format to 6,5,6,5 so that as many decimals as possible are recorded from the PSL program for your graphs. Next go to RUN EXPERIMENT and Calibrate your distance probe. Check the Room Temperature with the thermometer on the back wall and maximize your Data Rate. Then escape back to Preview and check that your machine has the correct COM port. If the PSL doesn't start, go to COM and change the port from 1 to 2 or vice-versa. Then return to Preview and verify that the probe is taking data.

A second member should verify that the probe can see the white book card attached to the bottom of the spring - just above the top of the milk jug. Note that only slight adjustments should be necessary!. When the spring is gently oscillated, the card should not rub against the container or twist violently. Note that the masses (750 grams total) MUST remain completely submerged in the water during each trial and NO water should be splashed out of the container. While the probe is in Preview, verify that the probe is seeing the card by moving the masses carefully up and down -- DO NOT USE LARGE AMPLITUDES! 5-6 cm is MORE THAN ENOUGH! When everything is working, escape from Preview and go to Start.

Procedure (data collection):

Since the spring needs a few seconds to stabilize, the person releasing the spring should tell the PSL operator when to start the probe. Try to release your spring with a small steady amplitude and a minimal amount of rotation (twisting). Watch your graphs. The oscillations should minimally have either a constant set of smooth crests OR smooth troughs -- it is not absolutely necessary to have perfect oscillations in both places. When you have a good trial, so to DATA, cursor down to Spreadsheet, press enter and then press F6 to change drives to A. Next press the grey insert key to save your first satisfactory trial. Use the following format for your filename: your period number, then aide letters, then WR1. For example a file in 4th period might look like: 4mnopWR1. REMEMBER that you do NOT put an extension on files in PSL, the program will add its own. Then type your group's last names as a description. Finally, carefully rerun the experiment and obtain a second trial. Save this one as WR2. Run your trials as accurately AND quickly as possible, remember that at least one other group needs to use your lab station before the period is over.

Record here both filenames and on which data disk your information is saved. Remember, do NOT remove a disk from the A drive until the green light is off - otherwise your files will not be saved correctly. You will analyze both of these data files tomorrow in class.

_________WR1             ___________WR2             data disk #_____

When you are finished with both trials, leave the spring, card & masses suspended in the water jug. Please wipe up any water that may have been dripped onto the table. F9 the PSL screen so that the next group can begin. Put these directions into the basket for safe keeping until tomorrow's class. DO NOT take them from the room. I need to use them this afternoon to correlate the data files.

Analysis (regression theory):

Input your data into the following EXCEL spreadsheet.  From there, we will determine the half-life of your damped oscillation.