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0000024115 00000 n The kinetic energy of the pendulum bob is given by 1 2 mv2. 0000003852 00000 n 0000040752 00000 n /Type /XObject

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Derivation of the equation of motion of the simple pendulum with a linear drag force is trivial, however, we present it here for completeness of the discussion. 0000004825 00000 n 0000063952 00000 n "6�`iczLx]��^S�T�c>��h6��k9��9��R1� F��$n�2� �֑��i��6��T6�`4�"�4^F�Fʆ`n:7FA�[�P��HP��*����RT5x-W��j1�ێ�|P* (@9�#h�6@P8�7A#(�2�`�6��2�h�ʒ��:�pr�����(�4��H�4��pu If we suspend a mass at the end of a piece of string, we have a simple pendulum. 0000028930 00000 n

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0000025710 00000 n 1135 0 obj <> endobj 0000114225 00000 n x�bb*e`b``Ń3� ���ţ�1�� WG. h�bbd```b``��� �ID2׃H�C`�o`� D���s��\���`�S`�#`�X0{#������ 2m���$cր��/ lg� �sG����H�y`6��P~�][A��X\Lڀt�t��r ��H����� �G�^��(�B�g`�r � ��& The variables we consider are mass, length of the pendulum, and angle of initial dislocation. 2.1 The Simple Pendulum . Square the values of the period measured for each length of the pendulum and record /Height 540

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Printer Friendly Version: Simple pendulums are sometimes used as an example of simple harmonic motion, SHM, since their motion is periodic.

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/Filter /FlateDecode sK$���"������"�fk�ɊU�B �m�#�o���+"���p0A �9�l�]W'������k�* �F3(���a�& tNt���H-ٸ�b�G(Ը=FgY�1�<. The period, T, of an object in simple harmonic motion is defined as the time for one complete cycle.

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They also fit the criteria that the bob's velocity is maximum as it passes through equilibrium and its acceleration is minimal while at each endpoint. If we suspend a mass at the end of a piece of string, we have a simple pendulum. 576 0 obj <> endobj x���xSu���v�Yf�_��A.Q�Eq(+#:P!.�@u\��%:Z'����*A��eȎA�+eG#����C,�ъ)h(���[�mR�6�y����CC�����'��;uu �+ t���t���eEQEu| ��� ��(���� ��(�"o�7(��(�"o�7(��(��Aޠ(��(�y��(��(�y��(���� ��(�"o�7(��(�"o�7(��(��Aޠ(��(����(��(�y��(���� ��(���� ��(�"o�7(��(��Aޠ(��(��Aޠ(��(�y��(��(�EQEQ� �EQE�7�EQE�7�EQE� oPEQy��AQEQy��AQEQ� �EQEQ� ��(���� ��(�"o�7(��(�"o�7(��(��Aޠ(��(�y��(��(�y��(��� %=== t�S�"ط���q � ��vuѢE�@_ @\��}�����f( � ��g��:u�G}�P � �OAA�ʕ+�� ������ǎ�8 � ��3�f4 � ��?ˊB�x��� �� ��mW�y��T�h � �o�ZYY٣G��'O2 } 1�?N-����P�/ �6l���� } q�t:���˄� } 1�o,�2eʮ]��� ����DŽ� } �ޮ2�"@_ @����������� b(�8�`����ӟ�� �*� �*� �\��Ƃn����_gd@_� +����i��ŋ32�/� ��v� � �]�cBE�� �T��Ԃ��~��Gap@_� ?

If all the mass is assumed to be concentrated at a point, we obtain the idealized simple pendulum.

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0000061263 00000 n You may assume that you are measuring from the lowest point. 0000027725 00000 n Figure 1(b) shows a simple pendulum with a bob of mass m and a total length L. The total drag force on the string and that on the bob of the pendulum are shown by F s and F b, respectively. 0000134609 00000 n 0000060717 00000 n 0000063493 00000 n FIGURE 2.1 The Simple Pendulum The Lagrangian derivation (e.g, [35]) of the equations of motion of the simple pen­ dulum yields: Iθ¨(t) + mgl sin θ(t) = Q, where I is the moment of inertia, and I = ml2 for the simple pendulum. 0 0000054161 00000 n �+�;3u�*J:�Xo���dTcH��hJ����j( %;:ВP���YZ��!��R@�d�(�,ˀJ! It was Galileo who first observed that the time 0000063798 00000 n x�b```a`�x�������A�؀�,S8�42�1��i�v�Sس�'CS�����C�Hl|"�J�-F7s�����Ţ1%t~�ޖL�e�/��w��9dJ���27�*e������Y�V��p�P�U��G�D8u:=]u}M������m+�^n�}{wk�ӇL��n��yM�ln;s?jm�Ӯ E�������Ȼ�#�#�����nN�"%;��� ۛ�h{P#�*���˾���ݚ�7k� E��)7����ۙd��R)�yq�U+��%^3��pj�ܹ�����b> `�3 �W��m ,5��~�}��$�� t�ap� 0000037759 00000 n

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11. Figure 1(b) shows a simple pendulum with a bob of mass m and a total length L. The total drag force on the string and that on the bob of the pendulum are shown by F s and F b, respectively. 0000022176 00000 n 0000137110 00000 n 0000045066 00000 n

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0000053398 00000 n 0000150810 00000 n startxref The equation of motion (Newton's second law) for the pendulum is . 0000020431 00000 n

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