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

AI Thread Summary
A pendulum clock exhibits moderate nonlinearity at small angles of displacement, and introducing friction does not alter the nonlinear behavior of the restoring force. The term "simple harmonic oscillator" applies strictly to systems with a linear restoring force, typically used in small angle approximations for pendulums. A user shared their experience of constructing a 2-D pendulum that visually records its displacement over time, raising questions about the accuracy of using the linear period equation T=2π(L/g)^(1/2) in the presence of friction. The discussion emphasizes the distinction between linear and nonlinear dynamics in pendulum motion. Understanding these concepts is crucial for accurately analyzing pendulum behavior in practical applications.
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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