1. Set the mass/spring system available at your table into oscillatory motion. Describe how you would measure the period of oscillation, using only a clock on the wall or your watch.

2. Try to make the mass oscillate with a very small amplitude. Use your watch or a clock on the wall to approximate the period and frequency of the oscillation and note it on your paper.

3. Now make the mass oscillate with a larger amplitude. Try to approximately double the amplitude that was used in question 2, but do not make the amplitude so large that the mass no longer oscillates smoothly. Again, use your watch or the clock on the wall to approximate the period and frequency of the oscillation and note it on your paper. Does increasing the amplitude have a significant effect on the period?

4. Use the motion detector and the mass and spring available at your table, along with the LoggerPro software to collect data on an oscillatory motion. Try to reproduce one of the smaller amplitudes you produced in the steps above. When taking data, remember that the motion detector cannot measure the position of anything closer than 0.5 meters away and always picks up the closest object (so keep your feet, legs, backpacks and the edge of the table out of the way). From the graph displayed, calculate the amplitude, period, and frequency.

Use the "analyze-examine" function of the software to get exact values.

5. Now make the mass oscillate with a larger amplitude. Try to approximately double the amplitude as compared to the step above, but do not make the amplitude so large that the mass no longer oscillates smoothly. Again, use the "analyze-examine" function of the software to precisely determine the amplitude, period and frequency of this oscillation. Does the period and/or frequency seem to depend on the amplitude of the oscillation? Are your approximate values for period and frequency from the steps above close the actual measure values here?

y = y_max cos(w t  + f) + zero offset

The "+ zero offset" term allows for the fact that your mass may not be oscillating about a height labeled as zero. Based on the your data from question 5, calculate the angular frequency, phase angle and zero offset. What is ymax?

7. We will now try to plot this model in LoggerPro. In order to do this, chose "data" from the tool bar across the top of the screen and then "modify column", and then "Model". You should see the following listed under equation: 1*COs(0*"time"+0)+0. Replace the 1's and 0's in this expression with your calculated values of ymax , w , f and zero offset. Click "ok" and see how well the model compares to your data. Repeat this process until you are satisfied with the fit of the model to your data. What is the complete and correct mathematical expression for the motion you recorded?

8. Now make the mass oscillate with a smaller amplitude. Try to approximately halve the amplitude as compared to the step above. Again, model the data with the mathematical expression, y = y_max COs(w t  + f) + zero offset, using the "data", "modify column", "Model" function as in the step above. What is the complete and correct mathematical expression for the motion?

9. Of the following features: ymax , w , f) and zero offset , which seemed to be the same for the motions studied in the two steps above? Which seemed to be different in the two different measurements?

10. State in your own words the physical meaning or significance of the each term in the equation: y = y_max COs(w t  + f) + zero offset