A pendulum bob oscillates between potential energy maxima at the top of its swing through kinetic energy maxima at the bottom of its swing. The potential energy is given by the mass times the height of the arc times gravitational acceleration and the kinetic energy maximum is given by the mass times the maximum velocity times the average velocity. Energy may be treated as a scalar in many phenomena, but here both energies are products of two vectors, fall direction and gravitation for potential energy and momentum times average velocity for kinetic energy. This nature of the pendulum is important.
The potential energy of the pendulum is equal to the work it can do under gravitational acceleration until its string is vertical. That work accelerates the pendulum bob to its maximum velocity. The kinetic energy of the pendulum is equal to the work it can do against gravitation to bring the pendulum bob to the top of its arc. It is posited that the shape of the atoms and molecules in the bob is the cause of its acceleration in the refraction gradient of a gravitational field, like a light path bending when passing a star. When the bob is free to move, their asymmetrical oscillations change the position of the bob as the process of falling. The response of the atoms and molecules in the bob to motion is to adjust their shape in order to remain in harmony with themselves, that is they shorten to enable complete oscillations despite translation. These shape changes together transfer potential energy to kinetic energy in the bob which is then available for the work of lifting the bob by reversing the changes in shape while decelerating. The key to this speculation is that reversible refraction or translation compensation actually move the location of internal oscillations in matter.
Dear friend Leonard Hall
While this speculation is interesting, it is not entirely accurate. The motion of a pendulum is due to the force of gravity acting on the mass of the bob, which causes it to oscillate back and forth. The potential energy of the pendulum is stored in the gravitational field, not in the shape of the atoms or molecules in the bob.
When the pendulum is released from its initial position, the potential energy is converted to kinetic energy as the bob accelerates toward the bottom of its swing. At the bottom of the swing, the kinetic energy is at its maximum and the potential energy is at its minimum. As the bob begins to swing back up, the kinetic energy is gradually converted back into potential energy until the bob reaches the top of its swing, where the potential energy is at its maximum and the kinetic energy is at its minimum. This process repeats as the pendulum oscillates back and forth.
While the shape of the atoms and molecules in the bob may affect its properties, such as its density or strength, they do not play a direct role in the motion of the pendulum. The motion of the pendulum is determined by the laws of physics, including the conservation of energy and the force of gravity.
Howdy Kaushik Shandilya,
Thank you for a clear expression of the standard description of a pendulum. It is good to have it stated up front in the discussion as an alternative to my speculation. The latter is an approach to explaining "What are kinetic and potential energy in oscillations?"
Your observation that my treatment of the pendulum is not entirely accurate may be "not entirely accurate" itself. The physical principles of refraction in a gravitational field and the shortening of an object so an oscillation could remain within it are quite respectable notions. To discover whether they apply here, or some better explanation of energy forms is available, is the purpose of this discussion. Please offer a better explanation to accompany your description - it will be welcome also.
Happy Trails, Len
Reflections on the pendulum led me to paper
Preprint Chaotic dynamics of an electron
And thinking about the principle of least action led me to the book
Research Proposal MATHEMATICAL NOTES ON THE NATURE OF THINGS
Howdy Igor Bayak,
Thank you for the opportunity to read your recent work, and also for looking into some of my writings. These references look interesting, and half-a-century ago, when I was gathering a sense of the world as revealed in equations, I would have read them more deeply. On perusal it seems you have a good, interesting approach to description and calculation of electrons, and further thought or interaction revealing your insights in discussion may lead to a deeper look.
For the moment, however, I do not find an answer to my question here, namely "What are kinetic and potential energy in oscillations?" That requires explanation which is fundamentally different from description or calculation. The Principle of Least Action also is not explanation (actually extreme action) but merely a reliable technique for calculations, despite the fact that the meaning and expression of "least action" have changed over the years. One must be careful and aware.
I offered what I would call an explanation in the question text. Do you have an opinion on the processes described there? Could they explain kinetic and potential energy in a pendulum, including the transfer of energy between them?
Happy Trails, Len
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