WangeneClock+Lab

=Clock Design: Simple Harmonic Motion= Date of Publication (Date of Most Recent Edits)


 * Participants**: Wangene.
 * Purpose**: The purpose of this lab is to design and characterize a clock that is makes accurate time measurements in the range of 30 to 90s.
 * Lab Documents**: [[file:Simple Harmonic Motion.doc]]


 * Brief Description Clock Design**: I designed a clock based on a mass/spring system. A bar system is used to suspend a coil, attached by way of a string. The masses rest on the coil, meaning the system is now comprised of a bar system, a vertically hanging coil and attached weights. The weights attached to the coil, logically, render it longer than it would be at resting position without the weights. The starting height for my bar system and coil were 13.7 cm, and with the weights the coils-mass construct was lowered to 3, meaning the coil system was being pulled down 10.7 cm and allowed to return to its starting position before measuring its lower position as one full cycle. The period of the clock is thus its motion between 3 cm on a metre stick up to 13.7 cm and back down to 3 cm, making one full bob. Although other ways to start the clock (mass/spring) could include lifting it up to a point I chose to pull it down because it clearly showed the limitations of my period. The time was measured by counting the number of bobs when the clock contained a certain mass-- I started out equating 10 bobs to approximately 10 seconds, realizing that ideally the period should equal 1 second if the clock were to be successful. I used number of bobs as my basis for measuring time, meaning it was a constant that remained to highlight other changes I made. The number of bobs I counted by interval of timing was 10, 20, 30, 40, 60, 75, 90 and 100.

(picture will be inserted here if found)


 * Specifications of Clock:** I started by creating a table for my data, recording: Weight, Original Height, Time and # of Bobs.

Chart:
 * Weight || Distance of Bob || Tim || # No. of Bobs ||
 * 500 g || 10.7 cm || 8.68 s || 10 ||
 * || 10.7 cm || 17.35 s || 20 ||
 * || 10.7 cm || 27.01 s || 30 ||
 * 600 g || 10.7 cm || 9.29 s || 10 ||
 * || 10.7 cm || 18.72 s || 20 ||
 * || 10.7 cm || 28.13 s || 30 ||
 * 700 g || 10.7 cm || 10.79 s || 10 ||
 * || 10.7 cm || 10.28 s || 10 ||
 * || 10.7 cm || 11.01 s || 10 ||  ||
 * 650 g || 10.7 cm || 10.21 s || 10 ||  ||
 * || 10.7 cm || 19.09 s || 20 ||  ||
 * || 10.7 cm || 28.84 s || 30 ||
 * || 10.7 cm || 38.77 s || 40 ||
 * || 10.7 cm || 57.73 s || 60 ||
 * || 10.7 cm || 72.32 s || 75 ||
 * || 10.7 cm || 87.00 s || 90 ||
 * || 10.7 cm || 96.8 s || 100 ||
 * || 10.7 cm || 96.8 s || 100 ||


 * Sample Calculations:**
 * //Speed calculation// || For the sake of uniformity, will reference speeds categorized by number of bobs & mass.

500 g for 10 bobs: s = 0.107 m/ 8.68 s = .012327 m/s

600 g for 10 bobs: s = 0.107 m/ 17.35 s = .00616 m/s

700 g for 10 bobs (averaged value): s = 0.107 m/ 10.69 s = .0104 m/s

650 g for 10 bobs: s = 0.107 m/10.21s = .0104 m/s

speed = distance / time

because the distance needed to travel is quite small compared to time, a standard is required. 10 cm is the baseline distance and it should be traveled in approximately 10 seconds. thus, period can be related in terms of speed, because it should go through its full cycle at a certain speed to be an accurate clock. when the observed speed is the closest to the standard, it is working most accurately as a clock. (again: 1 period means from its low point, to its high point, then back again to its low point)

s = 10 cm/10 secs s = .001 m/s for accurate clock ||
 * Design Variables:** I predicted that design variables such as the coil, how far the mass is pulled, the mass of the bob and the connection of the coil to the support beam would influence the operation of the clock. I thought that it the coil was would more tightly, the frequency would be greater. I thought that a larger pull on the mass would lead to a larger period, therefore a lower frequency. I thought that a larger weight would lead to a larger volume, and that if the system was connected to more points on the support beam, it would lead to less overall motion.


 * Studied Design Variable 1:** The design variable I studied was the mass of the bob-- as in independent variable that I changed, I observed that the time (as the dependent variable) corresponded accordingly. Increasing the mass did indeed lead to a larger period, which was proven by the fact that the mass took more time to make a full cycle at higher weights. At 500 g, it took less time to complete 10 bobs, because the period was smaller. At 700 g, it took more than 10 seconds to make 10 bobs.

Again, the bobs were measured by pulling the masses down approximately 10 cm and measuring how long it took in seconds for a set number of bobs to occur.

graph:

An event that lasts for a minute could be measured by the clock I created if the accuracy of the clock was improved. At 690 g, the weight shows a slightly more precise correlation of time and number of bobs, but the data I collected for this trial run proved insufficient to include in this report. Others who undertook a similar procedure also noted that 690 g allows the most precise measurement of data, where the object's period is related to each second.For the event puported to last 1 minute, the clock would be weighted with 690 grams and be lifted approximately 5 inches (returning it to the original position of the unweighted coil)
 * Lab Questions**: Write out and answer any questions that are included as a part of the lab.
 * 1) Describe in detail how your device may be used to measure an event that lasts 60s. What would the accuracy of this measurement be?

2. Which variable that you studied had the most significant effect on the frequency/period of the clock? If you built your clock with a 20% increase in this variable, what would the new frequency/period of the clock be? Support your answer by referring to data in your report. I only studied the most significant variable, which I found to be mass, for this clock design. If the mass was increased to 20% more than its original price, it would be 780 g, which would severely affect the function of the clock. The period for the clock at 700 g proved to be higher than the expected, and any increase in weight would correspondingly decrease its accuracy. The frequency of the clock's coil wouldn't change significantly with an increased massed, but the period would not remain unchanged. The accuracy of the data could be improved if the length that the coil traveled was standardized at 10.0, which would alleviate the slight awkwardness of interpreting results. Furthermore, if time had allowed me to collect more data across a wide spectrum of weights

3. Though it was not a project requirement, it would be nice if your clock could also measure much longer times, on the order of 10 to 15 minutes. Would your clock design still be accurate for long time measurements? What might affect the accuracy of the clock for these longer measurements? Can you think of a way to improve the design to make the clock more accurate for longer measurements? The clock design that I produced would not be accurate for longer measurements because I noticed in the bobs a decreasing bias with increasing time. This, I believe is caused by the friction of the coil, whose period decreases with time. At the beginning of the measurement, the mass would make a complete bob of appromiximately 10.7 cms, but with time, the period (or length that the mass falls to complete the bob) decreased until it eventually stopped moving. This means that the accuracy would gradually decrease with time unless the decrease in motion, due to friction, was compensated for by adding more weight (this would correlate with time) or manually ensuring the movement of the bob remained constant (this would be done by pulling the mass to its intended position at intervals, without disrupting the motion of its period.


 * Conclusion**

This experiment produced a valid, reproducible result, in that when the mass is increased 130% (in the case of 500 g to 650 g) the time it takes to complete a period also increases, by about 107%. The correlation of data proves that increase in mass accompanies an increase in time needed to complete a period.
 * The experimental results differ from my expected results because the experiment was not completely controlled-- the mass swung in a way that slightly interferred with its vertical motion; if the mass had been stabilized, the accuracy of the experiment could have improved somewhat. Also, I could not repeatedly test points-- due to lack of time. If I had also been able to test multiple variable, I could have fine tuned the experiment to include both variables, for maximum exactness.
 * A simple improvement to the experiment could be acheived by attaining weights that connect to each other in a way that balances the weight evenly (such as cylinders that interlock or act like magnets). This could reduce the swinging motion that causes further inaccuracy. Also, a coil that could be altered in frequency might increase accuracy.


 * //Don't forget to link to your lab report from the lab reports page and to include a link to your lab report in your reflection.//