Why is a simple pendulum not a perfect simple harmonic oscillator?

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Discussion Overview

The discussion revolves around the reasons why a simple pendulum is not considered a perfect simple harmonic oscillator, exploring the underlying mechanics and approximations involved in its motion.

Discussion Character

  • Debate/contested

Main Points Raised

  • Some participants reference Khan Academy's claim that a simple pendulum is not a perfect simple harmonic oscillator, questioning the validity of this assertion.
  • One participant asks whether the restoring torque is exactly proportional to the angle of the pendulum and what occurs at larger angles.
  • Another participant states that the restoring force is not exactly (negatively) proportional to the displacement, implying a deviation from simple harmonic motion.
  • A participant provides links to resources that offer better approximations for the period of a pendulum, suggesting that the standard model may not fully capture its behavior.
  • It is noted that while the simple pendulum does not behave as a simple harmonic oscillator, Christiaan Huygens's pendulum is mentioned as an example that follows the tautochrone curve and has an amplitude-independent period.

Areas of Agreement / Disagreement

Participants generally agree that the simple pendulum does not function as a perfect simple harmonic oscillator, but there are multiple competing views regarding the specifics of its behavior and the implications of different pendulum models.

Contextual Notes

There are unresolved questions about the assumptions regarding the proportionality of restoring forces and the effects of larger angles on pendulum motion. The discussion also references approximations that may not be universally accepted.

Huzaifa
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Khan Academy claims that a simple pendulum not a perfect simple harmonic oscillator. Why is it so?
 
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Huzaifa said:
Khan Academy claims that a simple pendulum not a perfect simple harmonic oscillator. Why is it so?
Is the restoring torque exactly proportional to the angle of the pendulum? What happens if the angle gets big?
 
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Because the restoring force is not exactly (negatively) proportional to the displacement.
 
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Yes, the simple pendulum is not a simple harmonic oscillator for reasons already explained. However, Christiaan Huygens's pendulum follows the tautochrone curve which is not as simple as a circle but has amplitude-independent period, i.e. is a simple harmonic oscillator.
 
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