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Motion of a Triple Rod Pendulum 
  • Harman,
  • Nick Nelson
Harman
California State University, Chico
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Nick Nelson
California State University, Chico
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Abstract

A Lagrangian approach to the triple pendulum is utilized to derive the equations of motion. Linearization of the Lagrangian near its stable equilibrium yields tractable equations of motion. The system's behavior is characterized by solving the matrix equation for its eigenfrequencies and eigenvectors. A python program, provided by Dr. Nelson, is utilized to model and plot the system behavior near its eigenfrequencies. A driving frequency near the eigenfrequency results in the system rapidly increasing in amplitude because of resonance. The steady-state solution of the system near its eigenfrequency results in beats. The beat frequency increases as the driving frequency deviates from the eigenfrequency slightly.