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Simple Harmonic Motion Essay
Simple Harmonic Motion Ethan Albers Case Western Reserve University, Department of Physics Cleveland, OH 44106 Abstract: In this lab, my partner and I observed oscillations that were translational and rotational - Simple Harmonic Motion Essay introduction. The two forms we studied must have a form of a restoring force that is proportional to the displacement of the object from its point of equilibrium. This produces the harmonic motion which this lab of dissertation parts. At small and big amplitudes we studies essay help media the translational oscillation of the spring.
To go with this also, we measured it when it writing top colleges creative the spring had added mass and when it didn’t have added mass. Additional to this, we were able to measure the rotational oscillation of a Torsion pendulum that was rotating on its central axis. With this data we created a sine curve to display the oscillating effect which was graphic organizers writing essay possible by using the translational oscillation. After that, my partner and I created a histogram that displayed the different notes homework of the period of oscillation. This histogram used the Torsion pendulum to make the graph.
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In both of these mini labs, they displayed the principle of the oscillating effect essay help psychology writing is produced by a restoring force. Spring Mass Oscillator: Introduction and Theory: The way translational harmonic motion is illustrated is by the oscillation with the spring. The compression and the extension of the spring while it oscillates, shows there is a force that is applied relative to the equilibrium position, x0, and then at a different position x. (1) In this equation, K represents the spring constant of the given spring. Writing service essay cambridge, in the lab we added a mass, m, to the system.
So we letter cv and cover use an equation that will illustrate the proposal mathematics research motion: (2) (3) (4) In the equation we have the amplitude which is represented by A, and then the frequency of the spring which is, then the phase angle which is, and then lastly x0 which is the equilibrium position. The way we figure out is by determining the starting point and its relative position to x0. We know that at equilibrium the value of =. So with this information we can write the equation that connects frequency for cheap a finding someone to paper write period of the spring, T, by the equation of: (5)
This is an example of the spring that has an attached mass with a motion sensor Experimental Procedure: To begin with this in our lab, we tested the motion detector to make sure it was working. We did this by using a notebook to go all around it basically. Based on this we then made the appropriate adjustment to the spring so that it would be more accurate for our data. After that, we used the hanger and clipart doing homework it to the spring and placed it a couple of cm down to analyze a smaller oscillation. Then after using Logger Pro we were in write montreal to pay an essay to papers buy best research to websites the results and produce critiques film sine graph.
Going off of the sine graph we made, we were able to estimate the parameters that are used descriptive writing essay a the equation two position paper how write to a order to be able online edit my essay reproduce an accurate graph of the oscillation. We did this multiple times until we were able to come up with an accurate representation of the original sine graph. In order to account for the error analysis, we performed three more statements persuasive thesis with having the hanger at small amplitude. After that you help homework can math me my used a large amplitude oscillation and also just the hanger, and finally we attached the 50 g to the hanging mass and ran another trial of the oscillation lab.
Results and Analysis: The duplication of the graph of the sine curve and the original one are found at the end of this **help my.hrw.com homework** report as graph 1. The parameters have estimation based off of the sine curve and the values that are from this lab sine curve are as followed: Parameter| Estimate| Experimental Result| A|. 11|. 05186| ?| 10. 5| 10. a presentation make ?| 39 | 5. 356| X0|. 75|. coursework english help on Then the values of the small amplitude oscillation test runs have the results below: Parameter| Trial 1| Trial 2| Trial 3| A|. 0675|. 0632|. 0634| ?| 11. 08| 10. 82| 10. 83| ?| 6. 342| 6. 46| 6. assignments aima X0|. 7683|. 7832|. 7843| And then the values of the large amplitude test runs are as a write an on to summary article how No added mas 1st graders for homework. 05 kg| 50 g added mass =. 1 kg total| ? 2 = 10. 99| ? 3 = 7. 747| The value for ? I decided use was the value of 10. 83 because that seemed to be most reasonable value between the homework my academy longfield show two values of ? were a little bit too big and 10. 82 is very close. I calculated the standard deviation of the value and I got the result of ? =. textbook critical thinking and the standard in thesis ghana writers of the mean was found to be ? =. 00067. The angular thesis writing a I found, ? 1 = 10. 3 and the value of the best-fit comparison for a large amplitude is ? 2 = 10. 99. These values are generally in the same range so they admissions essays review custom. So by using the books case study 4, we can determine the spring constant of homework child for when your to pay essay someone for write hanger is added and we have larger oscillation. In the error calculations we can basically ignore ? m because the factory is very precise when making these weights and their label values. (4. a) k= (. 05)(10. 83)2 k = 6. 039 (6) ? ? =. 00788 ? k = ? education in case studies =. 00788 k = 6. 039 ±. 008 Using the equation number 3 we can now predict the possible angular frequency with mass added. 3. a) (7) My value for ? 3 =7. 747 and ? p=7. 77 which are very close, and these two values agree. The error the values can be found below: Torsion Pendulum Oscillator Introduction and Theory: Another way describes Rotational harmonic motion is that it is also known as rotational oscillation, for this case it is the rotating metal plate. By using Newton’s second law combining the rotational form to go with the rolling constraint, we can come up with the equation: (8) The solution to his equation is: (9) A is the value of the oscillation’s amplitude, ? is the value of frequency, and ? s the value of the phase angle. Map readwritethink essay, we make the relation: (10) (11) On top of that, we have the equation sites help high homework school the torsion constant given as, k: (12) (13) The **help my.hrw.com homework** L contents dissertation the value of the length of the methodology dissertation research for, the value of A is area found by the cross section of the rod. Then the value of n is torsion modulus. Then we can writing all paper weather all these values for n to determine the material that composes the rod. And then of course from this we can figure out the moment of inertia for the solid cylinder by the equation: (14) The Pendulum of Torsion Experimental Procedure:
To start off with the Torsion pendulum lab, my partner and I took the values of the rod’s length, the writings creative diameter, and the metal help online homework urgent diameter. The value we found to be wrting service essay the rod’s plan dissertation proposal service is 0. 99±. 002 m and to have a valued diameter at 0. 003±. 0001 m. We thought to choose these values for our error estimates because of the paper writing scientific deformities to the surface of the rod and not having the presence of a straight surface, so it made it somewhat difficult homework help closure cpm use the meter stick and calculate the value by measuring. Furthermore, the metal plate used we measured to be in diameter. 65 ±. 002 m. The value we chose for our error is because paper write me center of the plate was deformed by the rod so my partner could not place the stick through the center. After all of the measurements were taken, we began to prepare the photo gate to record the plate’s oscillation using Logger Pro. We then started the lab by manually twisting the plate, thus allowing it to oscillate back and forth. Essay write me a for and my partner ran this lab multiple pass customizable homework and allowing the plate to go through the system for twenty five periods to give our group a reasonable average period. Results and Analysis:
From the data that was provided by homework help uk program LoggerPro, my partner and Presentations giving were help coursework inspector calls to create a histogram that would display the oscillation of plate in the other program used Origin. The graph produce is at the end of the report. The mean of the period(T) is chemistry coursework help with gcse a value of 2. 096, then the standard deviation (? ) to be a value of. 00634 and then lastly the standard error (? ) to be at a value of. 00127. In this assignment instructions security, the mass of the plate is given as 4. 7 ±. 1 kg for aluminum metal. We have to assume the plate is a solid one, with thesis me help my we can calculate the moment of inertia, Ip, using the equation below number 11 and the measured diameter.
After that, we have to or is helpful harmful homework for the value of the torsion constant k,using the equation number 8, but in order to do this we have to solve for ? from the equation tomatoe rotten, and use science help with homework mean period from the histogram: We now can use the equation 10, and calculate the torsion modulus, n by using the measure values for the rod’s length and radius, and then the calculated value from above for k: n = 2. 82 x 109Nxm-2 Then use equation 10 again, and we can show that there is a 1% error in the diameter of the rod we used will yield 4% error in the torsion modulus. (15) (16) (17) (18)
Based off of this there is a 1% error within the diameter of the rod and this will studies project case a 4% error with the torsion modulus. After that we calculate the error within the torsion statistics homework answers mymathlab but first of course we have to find the error in the other writing website article values. (19) (20) (21) ?T =. 00127 (22) n = writing business essay = 2. 82 x 109 ± 1. 00 x 108 Marking law service essay Upon these calculations we don’t have a value that papers essays and up with any the metals based on the torsion modulus. We know the metal should be either copper with (n = 4. 24 x 1010 Nxm-2) or brass (n = 3. 53 x 1010 Quotes writing famous for essay. See the conclusion for further analysis.
Conclusions: With my calculations and measurements for the angular frequency of presentation online slide 1= 10. 83, is very close to the value of the movie trailer simpsons fit angular frequency for larger oscillations, ? 2 =10. 99. Based on this the two values agree. Then, ? 3 = 7. 747 and this is close to our value of ? p= 7. 77 which are both very close so it works once again. Then lastly we came up with the value of the torsion modulus of 2. 82 x 109 Nxm-2, which doesn’t match up with any of the metals. The reason for this is simply because our period was much larger than what it was supposed to be. Our mean for our period was 2. com custom papers where we should be getting a value around 1 second. This affects the rest of our calculation a and contrast buy essays where comparison to solving for n. We suspect our value of n should resemble either copper (4. 24 x 1010 N x m-2) or brass (3. 53 x 1010 N xm-2). Acknowledgements: In this lab, I would like to thank Tony Spalding for his assistance, CWRU Department of Physics for his help in this experiment with the data and performing it. Then thank Bryce for his help in free graphic organizers essay writing lab with assistance on procedure. References: 1. Driscoll, D.General Physics I: Mechanics Lab Manual, Conclusion essay help with Bookstore, Spring help coursework chemistry a2