/A /Rect [147.6493 204.4084 196.0435 218.3262] << but in case of amplitude, the amplitude is excluded because acceleration is, the reason you gave brings me to my original question that, mass is excluded because gravitational acceleration is, The force of gravity acts down while the force which accelerates the pendulum is tangential to its circular motion. /Type /Encoding >> /Rect [147.6493 557.8096 158.6082 571.7274] << 9 0 obj >> /Border [0 0 0] << 7 0 obj where mis the mass and kis the spring constant (the stiffness). Period and frequency of a pendulum doesn't depend on mass? The acceleration towards the rest position is not constant but is proportional to the displacement. If you split the weight into two parts that are now hung off two separate connections, the weights will fall at the same rate as the big combined weight. Okay...The time period of a pendulum is independant of its mass and amplitude.For the "independance of mass",the reason is that, for same amplitude (distance from mean position), any change in mass would have no effect on the acceleration of the mass (gravitational acceleration is constant);hence the mass will reach the mean position at same time...But for the "independance of amplitude'', the reason I found is that, for a same mass, increase in amplitude would result in increase in restoring force, which would result in increase in acceleration; increased distance would increase acceleration and hence the mass will reach the mean position at the same time...Now my question is that, are'nt these two reasons contradictory, like one says that acceleration remains constant and the other states that the acceleration would increase?? /Subtype /Link endobj You will probably be 'merged'! Okay...The time period of a pendulum is independant of its mass and amplitude. �hvȭ8�V�`W�@�ѓx��z�; �F�0�~�������Ԑ�Dx��f:L3$?Zkd1��A�� Uƿx3�Y�wsH�9�!���s�/Cx0��Ԕ{�?����?ed]��z���B}�g�G���f�ka>��B��k��D��%�"֚�\�3��'�o]vw�.$�p���mEi���������?Ex��WH+ >> /D [5 0 R /Fit] /Subtype /Link
Well, it isn't exactly true for a pendulum. endobj /Differences [1 /dotaccent /fi /fl 33 /exclam 36 /dollar /percent 39 /quoteright /parenleft /parenright 44 /comma /hyphen /period /slash /zero /one /two /three /four /five /six /seven /eight /nine /colon /semicolon 61 /equal 63 /question 65 /A /B /C /D /E /F /G /H /I /J /K /L /M /N /O /P /Q /R /S /T /U /V /W 89 /Y 91 /bracketleft 93 /bracketright 95 /underscore /quoteleft /a /b /c /d /e /f /g /h /i /j /k /l /m /n /o /p /q /r /s /t /u /v /w /x /y /z 136 /circumflex 150 /endash] The period is completely independent of other factors, such as mass. Plotting the graph of pendulum period versus length, Periodic force applied to pendulum-like motion. >> Can you give me a valid reason as to why the time period does not (or a little) depend upon the mass of the bob??? /A ,"Vؾ�����H��L$��9y�����>z!qgc�r��.��^����0u���H*aPk�1(�E�t��U� << You have more or less described what goes on but what you can't 'prove' that way is how that effect produces equal time periods of cycles of all amplitudes. So, imagine the pendulum is at a horizontal 90 degree position (extreme case, but just for illustration). For a better experience, please enable JavaScript in your browser before proceeding. The period of a simple pendulum is [latex]T=2\pi\sqrt{\frac{L}{g}}\\[/latex], where L is the length of the string … /S /GoTo /Border [0 0 0] 16 0 obj I think you may have Mod trouble for posting about the same topic on two threads. stream /Type /Annot /Subtype /Link /Type /Annot
How do I measure a the period of a bifilar pendulum? Such objects will undergo simple harmonic motion /A x^mTˎ�0��+�$��`;!� ��
h�WH �� �~�:H�=�*�vWU�����~���Ɏ�w)�mS�]fG��c�*��l�~X�ۼ_m��U�b��ֻ�hߨxWf�{n�����(_%�Ã�=2n$��P�W�xq��q�Y�U��]JIĦ����M0�^ĸww.���H��@i�Y럘�n�������]y��8�oZlZ�`/o������E��������B˥�홺P���͊q����$Ou��Ϫ�6�1��X^lK��v�l�����n����ΨV��&jI�7�[&�k"�!�"��z6!B���}�0���I8�g��I�AlPm���-QH8�0�R��� Even simple pendulum clocks can be finely adjusted and accurate. The length of the pendulum is directly correlated to its period as per the pendulum equation: T = 2π√(L/g), where T is the period of the pendulum, L is its length, and g is the gravitational constant 9.8 m/s 2. endobj It seem like a lot of this could be address quite simply with the relevant diagram and associated differential equation of motion. stream /S /GoTo /A endobj That aspect I feel is a bit more obvious. /S /GoTo /Length3 0 >> The time period of oscillation of a given pendulum is constant. � ��L\\\�d {O'Ks �
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That has to use the Calculus. >> << /A A simple pendulum can be made by tying about one metre long thread to a small metal ball (called bob) and suspending it from a rigid support so that the bob is free to swing When the pendulum is … The only things that affect the period of a simple pendulum are its length and the acceleration due to gravity.
>> ... To begin our analysis, we will start with a study of the properties of force and acceleration in a simple pendulum by examining a freebody diagram of a pendulum bob. %PDF-1.4 Is there some reason why math is being avoided here? /Border [0 0 0] ��G�r�D�� Damping effect of swinging pendulum affect period?
>> Simple Harmonic Motion is only followed when the restoring force is exactly proportional to displacement - as with a steel clock spring. <<
/D [5 0 R /Fit] /A endobj << << This force is F, A hint of new physics in polarized radiation from the early universe, Neutrinos yield first experimental evidence of catalyzed fusion dominant in many stars, Understanding the utility of plasmas for medical applications, Why doesn't mass of a pendulum effect its time period. 18 0 obj /D [10 0 R /Fit] /D [5 0 R /Fit]
15 0 obj /Rect [221.6431 346.377 232.602 360.2949] endstream Comparing the two equations produces this correspondence: x→θ; k m → g l. Since the oscillation period for the ideal spring is T= 2π r m k, the oscillation period for the pendulum, in the θ→0limit, is T= 2π s l g. >>
/Border [0 0 0] /S /GoTo /Border [0 0 0] /Rect [205.2047 346.377 216.1636 360.2949] The precise definition of a simple ... law, for which the constant “c” in the above equation is the spring constant, 2. When the amplitude of the pendulum increases, the direction of these two forces gets more similar which means that a larger component of the force of gravity is rotating the pendulum. >> >> /Filter /FlateDecode /Rect [264.5456 204.4084 312.9399 218.3262] I mean, disregarding friction, all objects accelerate at the same rate towards earth, independent of mass. /S /GoTo /Length 654
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<< /Subtype /Link << << endobj Two threads have been merged as the issue could possibly be solved for both.
>>
Simple pendulum and properties of simple harmonic motion, virtual lab ... definite intervals of time called the period, T, it a periodic motion. endobj Derivation: Period of a Simple Pendulum. /Type /Annot This result is interesting because of its simplicity. 6 0 obj >>
/Type /Annot x^��ct�]�.�1:�S�m۶��mtlu:�ѱm��tl�֗�������_��5ƽ&�9ךs^�ZEF��B'djo��s�c�g��)k(���Z���)����l�dd"N@#K{;Q# 7@h /Subtype /Link /Length 24464 endobj The period for a simple pendulum does not depend on the mass or the initial anglular displacement, but depends only on the length L of the string and the value of the gravitational field strength g, according to The mpeg movie at left (39.5 kB) shows two pendula, with different lengths. /S /GoTo 8 0 obj
/Filter /FlateDecode JavaScript is disabled. This is an exception, because both questions are closely related. >> /Length2 23617 /Border [0 0 0] <<
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