Find the natural frequency of a system of two pendulums

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SUMMARY

The discussion focuses on determining the natural frequency of a coupled system of two pendulums connected by a spring. Key equations involved include the acceleration formula a = -gx/l and the period formula T = 2π√(l/g). Participants emphasize the necessity of deriving two equations of motion for each pendulum and suggest using free body diagrams to analyze forces acting on the pendulum bobs. The conversation highlights the importance of visualizing the system and considering the displacement of the pendulums.

PREREQUISITES
  • Understanding of simple harmonic motion and natural frequency
  • Familiarity with pendulum dynamics and the equations of motion
  • Knowledge of free body diagrams and force analysis
  • Basic concepts of coupled oscillators and spring mechanics
NEXT STEPS
  • Study the derivation of equations of motion for coupled pendulums
  • Learn about the method of free body diagrams in dynamic systems
  • Explore the concept of normal modes in coupled oscillators
  • Investigate the effects of spring constants on the natural frequency of oscillating systems
USEFUL FOR

Physics students, mechanical engineers, and anyone interested in understanding the dynamics of coupled oscillating systems.

joker_900
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Homework Statement


OK I haven't been given a definite question with values, but how would you find the natural frequency of a system of two pendulums coupled by a spring?


Homework Equations


a= -gx/l
T=2pi sqrt(l/g)


The Attempt at a Solution


Well the thing is, I know I need to consider each pendulum/spring separately and get two equations of motion, but I'm not sure how. All i know about pendulums are those two equations above. When I've had similar problems with springs I've been able to find the resultant force as a function of x and go from there. But in this case I just came up with the resultant -mgx/l - lamda(x-0.5l) = ma

Help!
 
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joker_900 said:
I know I need to consider each pendulum/spring separately and get two equations of motion, but I'm not sure how.

Some thoughts:
Have you drawn out a picture of the system? Are the pedulums fixed at the same point at the top or are their top points separated by the natural length of the spring?

Then: Can you use free body diagrams to find out the forces on the bobs of the pendulums? What if you displace one bob in the system by a small angle?
 

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