Wave Mechanics Problem Double Pendulum and a Spring

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SUMMARY

The discussion centers on modeling a double pendulum system with a spring under the influence of a driving force applied to masses m1 and m2. To analyze this system, participants suggest using the net energy approach, incorporating both kinetic and potential energies, and differentiating the energy function to find relationships between acceleration (a) and displacement (x). It is emphasized that if a continuous force acts on the system, the net energy is not constant due to the work-energy principle.

PREREQUISITES
  • Understanding of double pendulum dynamics
  • Familiarity with kinetic and potential energy concepts
  • Knowledge of differentiation in calculus
  • Basic principles of wave mechanics
NEXT STEPS
  • Study the equations of motion for double pendulums
  • Learn about the work-energy theorem in physics
  • Explore energy conservation principles in dynamic systems
  • Investigate numerical methods for simulating pendulum systems
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Students in wave mechanics, physics enthusiasts, and anyone interested in understanding complex dynamic systems like double pendulums and their response to external forces.

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I'm in a wave mechanics class and a homework assignment asks us to describe what would happen if a driving force is applied to m1, m2, or both. The explanation should be both calculational and written. I have no idea how to model this system in equation form! Help!
 

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Although you could analyse the situation using the equations of dynamics a simpler way is to write the net energy of the system at a general point in its path(which would include kinetic and potential energies) and differentiate the function and then put it equal to zero since the energy of the system remains constant.That should tell you the relation b/w a and x.
Note-If a force continuously acts on the system the net energy content of the system is not constant since you have work energy coming into the system.
 

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