Unless otherwise noted, LibreTexts content is licensed by CC BY-NC-SA 3.0. Additionally, a protractor could be taped to the top of the pendulum stand, with the ruler taped to the protractor. Other variables such as the angle of displacement were kept We built the pendulum with a length \(L=1.0000\pm 0.0005\text{m}\) that was measured with a ruler with \(1\text{mm}\) graduations (thus a negligible uncertainty in \(L\)). 293 0 obj <>/Filter/FlateDecode/ID[<38EF5019FD88AB4F9C00AFFA39D8A24A>]/Index[268 56]/Info 267 0 R/Length 106/Prev 171533/Root 269 0 R/Size 324/Type/XRef/W[1 2 1]>>stream The thin string used and a large mass reduces frictional effects and air drag. This was calculated using the mean of the values of g from the last column and the corresponding standard deviation. Thus, by measuring the period of a pendulum as well as its length, we can determine the value of \(g\): \[\begin{aligned} g=\frac{4\pi^{2}L}{T^{2}}\end{aligned}\] We assumed that the frequency and period of the pendulum depend on the length of the pendulum string, rather than the angle from which it was dropped. We measured \(g = 7.65\pm 0.378\text{m/s}^{2}\). 323 0 obj <>stream In this experiment, we measured \(g\) by measuring the period of a pendulum of a known length. Legal. Abstract. The period for one oscillation, based on our value of \(L\) and the accepted value for \(g\), is expected to be \(T=2.0\text{s}\). Aim: To determine acceleration due to gravity by measuring the time period of a simple pendulum. We repeated this measurement five times. Physics Report - Simple Pendulum - Free download as Word Doc (.doc / .docx), PDF File (.pdf), Text File (.txt) or read online for free. The uncertainty is given by half of the smallest division of the ruler that we used. This way, the pendulum could be dropped from a near-perfect \(90^{\circ}\) rather than a rough estimate. endstream endobj startxref We also worry that we were not able to accurately measure the angle from which the pendulum was released, as we did not use a protractor. BEST LAB REPORTS ONLINE. The Simple Pendulum is a basic time-keeping apparatus. The Simple Pendulum Laboratory Report. In the case of our lab , the monofilament fishing line we will use is a very close approximation to a massless string. The Simple Pendulum Revised 10/25/2000 4 Figure 2. %%EOF The corresponding value of \(g\) for each of these trials was calculated. Free LibreFest conference on November 4-6! Lab 1: Simple Pendulum 2 Now consider the dynamics of a simple pendulum, in Figure 1, below: Figure 1: Forces on a simple pendulum For rotational motion, τ = Iα, where α = θ¨ (angular acceleration), so we have −(mgsinθ)l = I¨θ= ml2θ¨, −gsinθ = lθ¨, θ¨+ g l sinθ =0. (s) Question 1: Are your results consistent with the hypothesis that the period of a pendulum is independent of its amplitude of oscillation? We expect that we can measure the time for \(20\) oscillations with an uncertainty of \(0.5\text{s}\). We transcribed the measurements from the cell-phone into a Jupyter Notebook. We thus expect to measure one oscillation with an uncertainty of \(0.025\text{s}\) (about \(1\)% relative uncertainty on the period). Have questions or comments? 268 0 obj <> endobj Our final measured value of \(g\) is \((7.65\pm 0.378)\text{m/s}^{2}\). 27.8: Sample lab report (Measuring g using a pendulum) Last updated; Save as PDF Page ID 19585; Contributed by Martin, Neary, Rinaldo, & Woodman; Assistant Professor (Physics) at Queen's University; Abstract; Theory; Predictions ; Procedure; Data and Analysis; Discussion and Conclusion; Abstract. The Simple Pendulum – 5 Report: The Simple Pendulum Name Partners Lab Station Date Table 1 — Dependence of Period on Amplitude Angle 5 10 15 20 30 40 50 60 # points mean T (s) std.

dev. We adjusted the knots so that the length of the pendulum was \(1.0000\pm0.0005\text{m}\). h�bbd``b`��@�)H�?���c HV�e2 �# � �`q-A,k6�P� �A�a,��@ˆ$�$t� ٝL�`m������� � e � The experiment was conducted in a laboratory indoors. The time period it takes to complete one swing is determined by the theoretical equation derived from the Physical Theory of Repeating Motions, aka Simple Harmonic Motion. Theory: A simple pendulum consists of a bob (a spherical mass) hung from a fixture by a very light string of length L. The mass of the string is much less than the mass of the bob.

The long pendulum arm and a small swing about a small angle help in the approximation of the simple harmonic motion. The LibreTexts libraries are Powered by MindTouch® and are supported by the Department of Education Open Textbook Pilot Project, the UC Davis Office of the Provost, the UC Davis Library, the California State University Affordable Learning Solutions Program, and Merlot. Discover everything Scribd has to offer, including books and audiobooks from major publishers. The model was supported by the data using a linear t with chi-squared If this experiment could be redone, measuring \(10\) oscillations of the pendulum, rather than \(20\) oscillations, could provide a more precise value of \(g\). The model was constructed with the square of the period of oscillations in the small angle approximation being proportional to the length of the pendulum. In the experiment, both the length and the mass of the bob were varied. Explain. h��Xmo�6�+�آ �w�@ ��5@�eq�0����D��`����wG�%�N�؊�B��;ɇϑ�VJ�U�Y(41 We plan to measure the period of one oscillation by measuring the time to it takes the pendulum to go through 20 oscillations and dividing that by 20. |6P�30�9�����[2L� iF �0 �?! The pendulum was released from \(90\) and its period was measured by filming the pendulum with a cell-phone camera and using the phone’s built-in time. This is consistent with the fact that our measured periods are systematically higher. �GS� @%�3�h �c`ivY� �,�3gDi rS0������x]L�)Pr3��!�m5)V����夘o�����x,כ����x� �.��b݄������?�V&;��� xT�1;/?��ӆXJ�~Qi�0�lv1?���.�M���gx�`���R�p�/Ƴr���f�,'��ɀ����i��ca����ή���w���lV���)��X��S�tW�&!���xZ>�����`S̾)���e�T1�U��,Vٟ~F�V��5D��qq5����r���a��F`̦_�=�|���`��� �1#m���j4:="`�� �Z��V��8�/��6=�~�1F�_�1/A��զ�&���[`C�Np�5�qg��D�0Q����(�-gŚ|.�&7��x^C�Tn�Pq���4����X1;�„��L,#7т\��e�v��e�j����B�K; �C���!�x$�P:R��OHlm. %PDF-1.5 %���� The experiment was carried out to show that the mass of the bob has no effect on the period of the oscillation. 0 C�P�Dj�PZ"(%*�P2�E%'y.��Qš"��T�3h� �[a�P��i&�b����QŒ ��A%njNv �Y��"�� Investigation of gravity and restoring force. h�b```���l� ��ea�X�$��pkMy\�N�s�J�V��h��b�xw�1��ۥ��ݵ�r�����ƻ;����� cXGG�2Gt0Ht00tt4�ft41��@ ��ĥ �ŁX,��Ϥ"�" ��:!��ic1�1��r�&��}���6X���v�C^�փE DOCX, PDF, TXT or read online from Scribd, 96% found this document useful (48 votes), 96% found this document useful, Mark this document as useful, 4% found this document not useful, Mark this document as not useful, Save Physics Report - Simple Pendulum For Later. The pendulum method is used for determination of the acceleration of gravity (g). This correspond to a relative difference of \(22\)% with the accepted value (\(9.8\text{m/s}^{2}\)), and our result is not consistent with the accepted value. All of our measured values were systematically lower than expected, as our measured periods were all systematically higher than the §\(2.0\text{s}\) that we expected from our prediction. The relative uncertainty on our measured value of \(g\) is \(4.9\)% and the relative difference with the accepted value of \(9.8\text{m/s}^{2}\) is \(22\)%, well above our relative uncertainty. We suspect that by using \(20\) oscillations, the pendulum slowed down due to friction, and this resulted in a deviation from simple harmonic motion. Using a simple pendulum the acceleration due to gravity in Salt Lake City, Utah, USA was found to be (9.8 +/- .1) m=s2. The period, \(T\), of a pendulum of length \(L\) undergoing simple harmonic motion is given by: \[\begin{aligned} T=2\pi \sqrt {\frac{L}{g}}\end{aligned}\]. We constructed the pendulum by attaching a inextensible string to a stand on one end and to a mass on the other end. A pendulum exhibits simple harmonic motion (SHM), which allowed us to measure the gravitational constant by measuring the period of the pendulum. This has a relative difference of \(22\)% with the accepted value and our measured value is not consistent with the accepted value. A weight is suspended on a length of string which in turn is attached to a frictionless pivot so it can swing freely. Register now! The simple pendulum is composed of a small spherical ball suspended by a long, light string which is attached to a support stand by a string clamp. Investigation of gravity and restoring force. Aim: To determine acceleration due to gravity by measuring the time period of a simple pendulum. We also acknowledge previous National Science Foundation support under grant numbers 1246120, 1525057, and 1413739. Using a \(100\text{g}\) mass and \(1.0\text{m}\) ruler stick, the period of \(20\) oscillations was measured over \(5\) trials.