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

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SUMMARY

A simple pendulum is not a perfect simple harmonic oscillator due to the non-linear relationship between the restoring torque and the angle of displacement. As the angle increases, the restoring force deviates from being directly proportional to the displacement, leading to inaccuracies in the oscillation period. In contrast, Christiaan Huygens's pendulum adheres to the tautochrone curve, exhibiting an amplitude-independent period and qualifying as a simple harmonic oscillator. For further insights, refer to the detailed analysis provided in the linked resources.

PREREQUISITES
  • Understanding of simple harmonic motion principles
  • Familiarity with torque and angular displacement concepts
  • Knowledge of pendulum mechanics
  • Basic grasp of mathematical approximations in physics
NEXT STEPS
  • Research the mathematical derivation of the period of a simple pendulum
  • Explore the properties of Christiaan Huygens's pendulum
  • Study the effects of large angles on pendulum motion
  • Learn about the tautochrone curve and its implications in oscillatory motion
USEFUL FOR

Physics students, educators, and anyone interested in the dynamics of oscillatory systems will benefit from this discussion, particularly those studying the limitations of simple harmonic motion in real-world applications.

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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