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Created the page with a small section on the history and physics of pendula
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".
==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.
==Physics of Pendula==
When the bob of the pendulum is at its lowest point, the pendulum is in [[equilibrium]] and is does not move. If the bob is moved slightly and released, the force of [[gravity]] acts on the pendulum trying to restore it to equilibrium and the pendulum will oscillate about this point. Despite the motion of a pendulum appearing to be very simple, the equation of motion for a particular pendulum cannot often be found exactly. Sometimes they can be expressed in terms of infinite [[Series (mathematics)|series]], otherwise approximations or numerical simulations using computers are used instead.
===The simple 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>
\ddot \theta = -\frac{g}{l} \sin{\theta}
</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:
<math>
P = 2 \pi \sqrt{\frac{g}{l}}
</math>
Interestingly, this means that for oscillations with small amplitudes, the period does not depend on the amplitude. In general, this is not true and it increases for larger amplitudes.
===The Foucault pendulum===
The [[Foucault's Pendulum|Foucault pendulum]] consists of a heavy mass hung from a long line. It is allowed to swing in only a single plane. As it oscillates, the [[earth]] rotates beneath it causing the plane of oscillation to change and so it is evidence that the [[earth]] rotates.
===The conical pendulum===
The conical pendulum is a system that can be solved exactly. The bob follows a circular path in a horizontal plane and so performs [[circular motion]].
==References==
<references/>
==See Also==
[[Clock]]s
[[Simple harmonic motion]]
[[Category:Physics]]
[[Category:Mechanics]]
==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.
==Physics of Pendula==
When the bob of the pendulum is at its lowest point, the pendulum is in [[equilibrium]] and is does not move. If the bob is moved slightly and released, the force of [[gravity]] acts on the pendulum trying to restore it to equilibrium and the pendulum will oscillate about this point. Despite the motion of a pendulum appearing to be very simple, the equation of motion for a particular pendulum cannot often be found exactly. Sometimes they can be expressed in terms of infinite [[Series (mathematics)|series]], otherwise approximations or numerical simulations using computers are used instead.
===The simple 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>
\ddot \theta = -\frac{g}{l} \sin{\theta}
</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:
<math>
P = 2 \pi \sqrt{\frac{g}{l}}
</math>
Interestingly, this means that for oscillations with small amplitudes, the period does not depend on the amplitude. In general, this is not true and it increases for larger amplitudes.
===The Foucault pendulum===
The [[Foucault's Pendulum|Foucault pendulum]] consists of a heavy mass hung from a long line. It is allowed to swing in only a single plane. As it oscillates, the [[earth]] rotates beneath it causing the plane of oscillation to change and so it is evidence that the [[earth]] rotates.
===The conical pendulum===
The conical pendulum is a system that can be solved exactly. The bob follows a circular path in a horizontal plane and so performs [[circular motion]].
==References==
<references/>
==See Also==
[[Clock]]s
[[Simple harmonic motion]]
[[Category:Physics]]
[[Category:Mechanics]]