Are all damped oscillations periodic?

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SUMMARY

Damped oscillations exhibit varying periodicity based on the damping regime. In the case of a free damped harmonic oscillator, motion is periodic only in the weakly damped regime; both strongly damped and critically damped regimes result in non-periodic motion. Additionally, undamped harmonic oscillators can demonstrate quasi-periodic motion depending on the irrationality of the frequency ratio. This establishes that not all damped oscillations are periodic.

PREREQUISITES
  • Understanding of damped harmonic oscillators
  • Knowledge of damping regimes: weakly damped, critically damped, and strongly damped
  • Familiarity with phase space dynamics
  • Basic concepts of frequency ratios and their implications
NEXT STEPS
  • Research the characteristics of weakly damped harmonic oscillators
  • Study critically damped and strongly damped systems in detail
  • Explore quasi-periodic motion in undamped harmonic oscillators
  • Investigate the mathematical implications of frequency ratios in oscillatory systems
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Physicists, engineers, and students studying oscillatory motion and dynamics, particularly those interested in the behavior of damped systems.

Himanshu_6174
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I know the equation for damped oscillation where the damping force depends on velocity. In that case the damped oscillation has a fixed angular frequency and thus time period! I am wondering if there are any types of damped oscillation where the time period is not constant i.e. the motion is not periodic!
 
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Himanshu_6174 said:
I am wondering if there are any types of damped oscillation where the time period is not constant i.e. the motion is not periodic!
For a free (i.e. non-driven) damped harmonic oscillator in the strongly damped or critically damped regime, the motion is not periodic. It's only periodic in the weakly damped regime.

If you consider a pair of undamped harmonic oscillators, then their phase space dynamics on the torus may display quasi-periodic (but not periodic) motion depending on the (ir)rationality of the ratio of their frequencies. This is probably the simplest example of non-periodic motion.
 
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