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Pendulum Types

Title text: The creepy fingers that grow from a vibrating cornstarch-water mix can be modeled as a chain of inverted vertical pendulums (DOI:10.1039/c4sm00265b) and are believed to be the fingers of Maxwell's Demon trying to push through into our universe.

Explanation

This explanation may be incomplete or incorrect: Created by CREEPING TENDRILS OF STARCH - Please change this comment when editing this page. Do NOT delete this tag too soon.

This comic shows and describes several pendulums. The first three are actual physics models, while the last one is made up for absurdity. This is a recurring format of xkcd comics, as shown in 2289: Scenario 4.

The simple pendulum consists of a joint, rod, and weight, and when released (inside a gravity field or other accelerating force), it swings in a regular fashion. The "period" of a pendulum is the amount of time it takes to complete one cycle, swinging back and forth. In a simple pendulum, the period is consistent, predictable, and depends primarily on the length of the pendulum (being largely independent of both mass and length of arc). This predictability makes pendulums useful in applications such as timekeeping, where the earliest accurate clocks (such as a grandfather clock) made use of pendulums as regulators.

The double pendulum consists of 2 joints, 2 rods, and a weight, and when released, it swings in a chaotic fashion. Interestingly, this follows by the mathematical definition of chaotic, being that small changes in initial conditions result in vast differences in end results. This pendulum is thus nearly unpredictable, and due to this chaotic nature, real life applications are very limited.

The inverted pendulum consists of a simple pendulum that is placed upside down, with some apparatus underneath vibrating it vertically to keep it upwards. If left unpowered (or improperly controlled from positional feedback) it will fall, hence the "unstable" part. (The comic, however, appears to depict Kapitza's pendulum, a powered version that does not rely upon monitoring and feedback control.)

The nightmare pendulum appears to be an inverted double pendulum, with an additional uninverted pendulum swinging within its much more substantial weight (which is also adorned with archaic/mystical symbols). The comic claims that this pendulum summons Maxwell's demon, jokingly implying that Maxwell’s demon is an actual entity. In fact, Maxwell's demon is a thought experiment in which a being - the demon -­­­­­ is posted at a tiny door between two gas vessels. It lets only slow-moving (cold) gas molecules move through the door in one direction, and only fast-moving (hot) ones in the other direction. One vessel gradually becomes hot and the other cold, appearing to violate the second law of thermodynamics. It doesn't, but the thought experiment has stimulated much discussion since it was first proposed by James Clerk Maxwell in 1867.

The title text continues this joke explicitly, by referencing a real paper titled Vibro-levitation and inverted pendulum: parametric resonance in vibrating droplets and soft materials and implying that the paper ties the "creepy fingers" produced in this way to Maxwell's demon. The paper only actually suggests that the phenomenon is related to inverted pendulum dynamics. This gives a humorous example for the abuse of citations. Technically, the cited reference only supports the claim immediately before it, that the behavior of a cornstarch-water mix (also known as oobleck) can be modeled as inverted pendulums. But by proximity the reference also seems to support the part about Maxwell's demon. The illusion is helped by the description of the cornstarch as creepy, which is added in the beginning without any visible separation from the actual content of the citation.

Transcript

[Four types of pendulums are shown in a single panel. Each has a bullet list below the depiction.]

[Label:]

Simple pendulum

[A basic pendulum consisting of a joint, rod, and weight swinging in a regular arc]

• Periodic
• Stable
• Useful for timekeeping

[Label:]

Double pendulum

[A pendulum consisting of 2 joints, 2 rods, and a weight swinging in a more loopy arc]

• Aperiodic
• Chaotic
• Moderately cursed

[Label:]

Inverted pendulum

[An upside-down basic pendulum with some apparatus underneath vibrating up and down]

• Finely balanced
• Unstable
• Becomes stable when vibrated

[Label:]

Nightmare pendulum

[An inverted double pendulum, with an additional uninverted pendulum swinging within a large weight adorned with archaic/mystical symbols]

• Forbidden
• Unphysical
• Summons Maxwell's Demon

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