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A '''pendulum''' is an object that is suspended from a pivot and allowed to swing.<ref name="Britannica">[https://www.britannica.com/technology/pendulum Britannica.com]</ref> Pendula are particular useful for making [[clock]]s as they have a regular period when they oscillate. The mass at the end of the pendulum is known as the "bob".

A '''pendulum''' is an object that is suspended from a pivot and allowed to swing.<ref name="Britannica">{{cite web|url=https://www.britannica.com/technology/pendulum|title=Pendulum|accessdate=2019-07-25|publisher=Britannica.com}}</ref> Pendula are particular useful for making [[clock]]s as they have a regular period when they oscillate. The mass at the end of the pendulum is known as the "bob".

==History==

==History==

The history of the pendulum began when [[Galileo Galilei]] timed the period of a swinging lamp in Pisa cathedral using his pulse. He found that the period did not appear to change and believed it could be used to make a clock.<ref name="Britannica"/> A pendulum was used to make a clock for the first time in 1656 by [[Christiaan Huygens]].<ref>[http://www.theclockdepot.com/clocks-blog/history-of-the-pendulum-clock/ theclockdepot.com]</ref> Pendulum based clocks remained the most accurate time keeping devices until the 1930s when quartz clocks were developed.

The history of the pendulum began when [[Galileo Galilei]] timed the period of a swinging lamp in Pisa cathedral using his pulse. He found that the period did not appear to change and believed it could be used to make a clock.<ref name="Britannica"/> A pendulum was used to make a clock for the first time in 1656 by [[Christiaan Huygens]].<ref>{{cite web|url=http://www.theclockdepot.com/clocks-blog/history-of-the-pendulum-clock/|title=History of the Pendulum Clock|accessdate=2019-07-25|publisher=theclockdepot.com|date=2010-07-15}}</ref> Pendulum based clocks remained the most accurate time keeping devices until the 1930s when quartz clocks were developed.

==Physics of Pendula==

==Physics of Pendula==

An example of an approximation is that of the simple pendulum. Here, a massless rod is used to connect the bob to its pivot, the bob is assumed to be a point particle and [[friction]] is neglected. The [[amplitude]] of the pendulum is the angle θ between the rod and the vertical and can be used to write an equation describing the motion of the pendulum:

An example of an approximation is that of the simple pendulum. Here, a massless rod is used to connect the bob to its pivot, the bob is assumed to be a point particle and [[friction]] is neglected. The [[amplitude]] of the pendulum is the angle θ between the rod and the vertical and can be used to write an equation describing the motion of the pendulum:

<math>

:<math>

\ddot \theta = -\frac{g}{l} \sin{\theta}

\ddot \theta = -\frac{g}{l} \sin{\theta}

</math>

</math>

where g is the [[acceleration due to Gravity|acceleration due to gravity]] and l is the length of the pendulum. Even this equation cannot be solved exactly and a further approximation can be made: that the amplitude of the pendulum is small (around a few degrees). Therefore, <math>\sin{\theta}</math> can be replaced with just θ meaning that the pendulum undergoes [[simple harmonic motion]]. The period can then be found as:

where g is the [[acceleration due to Gravity|acceleration due to gravity]] and l is the length of the pendulum. Even this equation cannot be solved exactly and a further approximation can be made: that the amplitude of the pendulum is small (around a few degrees). Therefore, <math>\sin{\theta}</math> can be replaced with just θ meaning that the pendulum undergoes [[simple harmonic motion]]. The period can then be found as:

<math>

:<math>

P = 2 \pi \sqrt{\frac{g}{l}}

P = 2 \pi \sqrt{\frac{g}{l}}

</math>

</math>

==References==

==References==

==See also==

==See also==