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

Click For Summary
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
Messages
40
Reaction score
2
Khan Academy claims that a simple pendulum not a perfect simple harmonic oscillator. Why is it so?
 
Physics news on Phys.org
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?
 
Because the restoring force is not exactly (negatively) proportional to the displacement.
 
Reply
  • Like
Likes olgerm and vanhees71
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.
 
Reply
  • Like
Likes Dadface, vanhees71, DaveE and 2 others

Thread 'Traveling through space at zero km/s'

In sci-fi when an author is talking about space travellers or describing the movement of galaxies they will say something like “movement in space only means anything in relation to another object”. Examples of this would be, a space ship moving away from earth at 100 km/s, or 2 galaxies moving towards each other at one light year per century. I think it would make it easier to describe movement in space if we had three axis that we all agree on and we used 0 km/s relative to the speed of...
View full post »

Similar threads

High School Harmonic oscillator and simple pendulum time period
  • · Replies 36 ·
2
Replies
36
Views
4K
Undergrad Thoughts about coupled harmonic oscillator system
  • · Replies 1 ·
Replies
1
Views
1K
High School Is the Motion of a Pendulum Described by a Harmonic Oscillator Model?
  • · Replies 12 ·
Replies
12
Views
2K
High School Forced Oscillations: Pendulum 1 Driving Neighboring Pendulum
  • · Replies 2 ·
Replies
2
Views
1K
Undergrad Alternative Approach to Solving Foucault's Pendulum Behavior
  • · Replies 8 ·
Replies
8
Views
2K
Undergrad Problem with the harmonic oscillator equation for small oscillations
  • · Replies 3 ·
Replies
3
Views
2K
Graduate Measurement uncertainty due to thermal noise
  • · Replies 4 ·
Replies
4
Views
2K
Graduate Flaw in Lagrangian Mechanics for a rotary inverted pendulum system? (Simulation vs. Measured)
  • · Replies 11 ·
Replies
11
Views
2K
Undergrad How Does Changing Mass and Spring Force Affect Watch Oscillators?
  • · Replies 11 ·
Replies
11
Views
2K
High School Why does my LC circuit not oscillate its energy between Electric & Magnetic fields?
  • · Replies 152 ·
6
Replies
152
Views
7K