Which is more linear, a frictionless or slightly frictional pendulum clock?

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SUMMARY

The discussion centers on the linearity of pendulum clocks, specifically comparing frictionless and slightly frictional models. It is established that a pendulum exhibits moderate nonlinearity at small angles of displacement, and the introduction of friction does not alter the nonlinear behavior of the restoring force. The term "simple harmonic oscillator" is defined strictly as a system with a linear restoring force, applicable under small angle approximations. Additionally, the linear period equation T=2π(L/g)^(1/2) can be used as a rough approximation even when friction is present.

PREREQUISITES
  • Understanding of simple harmonic motion
  • Knowledge of pendulum mechanics
  • Familiarity with linear and nonlinear systems
  • Basic grasp of damping effects in oscillatory systems
NEXT STEPS
  • Research the effects of damping on pendulum motion
  • Explore the mathematical derivation of the linear period equation T=2π(L/g)^(1/2)
  • Study the differences between linear and nonlinear restoring forces
  • Investigate experimental setups for observing pendulum motion and displacement
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Physics students, mechanical engineers, and hobbyists interested in pendulum mechanics and oscillatory systems.

Loren Booda
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A pendulum (clock) is moderately nonlinear for small angles of displacement. Is simple harmonic motion better approached by introducing a degree of friction into its works?
 
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I'm not sure what you mean by "moderately nonlinear" but, no, you won't change the way that the nonlinear "restoring force" behaves by adding damping. Perhaps you're confusing "nonlinear" with "unstable?"

Incidentally, the expression "simple harmonic oscillator" refers ONLY to a system with a linear restoring force and is often used in the small angle approximation to a pendulum.
 
Tide,

I helped a young man construct a 2-D pendulum whose bob traces out in sand its displacement vs time. It swings discernably for about ten cycles (a total of ~17 seconds), leaving both a record of its displacement and the number of periods. Is it a safe, albeit rough, approximation to use the linear period equation T=2pi(L/g)1/2 when such friction is involved?
 

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