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Subhasish Mandal
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what is the relation between the energy &time period of a pendulam while not considering the small angle approximation,the given potential v(x)=Asinx
Energy and Time Period of a Pendulum in Simple Harmonic Motion
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SUMMARY
The relationship between energy and the time period of a pendulum in simple harmonic motion, without the small angle approximation, involves the potential function v(x) = A sin(x). This topic is explored in depth in "Berkeley Mechanics" by Kittel, where elliptic functions are likely utilized to derive the necessary equations. The discussion emphasizes the mathematical complexity of the problem and the importance of consulting established physics texts for a comprehensive understanding.
PREREQUISITES- Understanding of simple harmonic motion principles
- Familiarity with potential energy functions
- Knowledge of elliptic functions
- Basic mathematical skills for manipulating equations
- Study the derivation of time periods for pendulums using elliptic functions
- Explore the potential energy functions in classical mechanics
- Read "Berkeley Mechanics" by Kittel for detailed explanations
- Investigate the effects of large angles on pendulum motion
Physics students, educators, and anyone interested in advanced mechanics and the mathematical modeling of pendulum motion.
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