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,��@$�$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$�P:R��OHlm. %PDF-1.5 %���� The experiment was carried out to show that the mass of the bob has no effect on the period of the oscillation. 0 C�P�Dj�PZ"(%*�P2�E%'y.��Qš"��T�3h� �[a�P��i&�b����Q ��A%ǌNv �Y��"�� Investigation of gravity and restoring force. h�b```���l� ��ea�X�$��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.