Two damped pendulums with different masses.

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SUMMARY

This discussion focuses on the dynamics of two damped pendulums with different masses, specifically where one pendulum has a mass m2 that is double that of the other, m1. Both pendulums have the same length L and are subjected to a damping force represented by Fdamp=-\gamma\dot{x}. The amplitude of the lighter pendulum decreases to half its initial value, and the equation A(t)/A0=e^(-\gamma t/2m) is introduced for analyzing amplitude decay over time.

PREREQUISITES
  • Understanding of damped harmonic motion
  • Familiarity with the equation of motion for pendulums
  • Knowledge of exponential decay functions
  • Basic grasp of the damping coefficient, γ
NEXT STEPS
  • Study the derivation of the damping force in pendulum systems
  • Explore the effects of mass on the damping rate in oscillatory systems
  • Learn how to apply the amplitude decay equation A(t)/A0=e^(-\gamma t/2m) in practical scenarios
  • Investigate the role of initial conditions in damped oscillations
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TheTourist
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Two simple pendulums with the same length L but different masses, m1 and m2=2*m1, are set swinging at the same time with the same initial amplitude. Both pendulums are damped by the same force, Fdamp=-[tex]\gamma[/tex]s(dot). Eventually, the amplitude of the lighter pendulum decreases to half its initial value.
[tex]\gamma[/tex]




I have found the equation [tex]\frac{A(t)}{Ao}[/tex]=e(-[tex]\gamma[/tex]t/2m), however I am not sure how to apply it correctly.
 
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