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A new pendulum motion with a suspended point near infinity.
A I Ismail1,2
1Mechanical Engineering Department, College of Engineering and Islamic Architecture, Umm Al-Qura University, P. O. Box 5555, Mecca, Saudi Arabia. aiismail@uqu.edu.sa.
Scientific Reports
|June 25, 2021
Summary
This study analyzes a pendulum on a spring with a moving suspension point. It uses Lagrange
Area of Science:
- Mechanical Engineering
- Applied Mathematics
- Physics
Background:
- Investigates a complex mechanical system: a simple pendulum suspended on a spring, allowing planar oscillations.
- The system's suspension point follows a circular path with a large radius.
- Two degrees of freedom describe the motion: pendulum's angular displacement and spring's extension.
Purpose of the Study:
- To derive and approximate the equations of motion for this two-degree-of-freedom system.
- To analyze the system's dynamics using a large parameter approximation, differing from previous small parameter studies.
- To explore the influence of system parameters on motion through computational analysis.
Main Methods:
- Utilized Lagrange's equation to derive the equations of motion.
- Employed an approximation method up to the third order using a large parameter.
- Conducted computerized simulations to analyze parameter influences.
Main Results:
- Obtained approximated solutions for the complex equations of motion.
- Demonstrated the impact of various system parameters on the pendulum's motion.
- Validated the computational methods through graphical representations.
Conclusions:
- The study successfully provides approximated solutions for a complex pendulum-spring system.
- The use of a large parameter approximation offers a novel approach to analyzing such systems.
- Computational analysis confirms the accuracy of the derived solutions and highlights parameter effects.
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