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A pendulum is a body suspended from a fixed support such that it freely swings back and forth under the influence of gravity. When a pendulum is displaced sideways from its resting, equilibrium position, it is subject to a restoring force due to gravity that will accelerate it back towards the equilibrium position.
In terms of energy, all systems have two types of energy: potential energy and kinetic energy. When a spring is stretched or compressed, it stores elastic potential energy, which is then transferred into kinetic energy. The potential energy within a spring is determined by the equation =.
Every conservative force has a potential energy. By following two principles one can consistently assign a non-relative value to U: Wherever the force is zero, its potential energy is defined to be zero as well. Whenever the force does work, potential energy is lost.
In the tautochrone problem, if the particle's position is parametrized by the arclength s(t) from the lowest point, the kinetic energy is then proportional to ˙, and the potential energy is proportional to the height h(s). One way the curve in the tautochrone problem can be an isochrone is if the Lagrangian is mathematically equivalent to a ...
The total energy is given by the sum of the kinetic and potential energies = + and the Lagrangian by their difference =. The total energy is conserved in a mathematical pendulum, so time t {\displaystyle t} dependence of the potential E P O T {\displaystyle E_{\mathrm {POT} }} and kinetic E K I N {\displaystyle E_{\mathrm {KIN} }} energies is ...
The pendulum reaches greatest kinetic energy and least potential energy when in the vertical position, because it will have the greatest speed and be nearest the Earth at this point. On the other hand, it will have its least kinetic energy and greatest potential energy at the extreme positions of its swing, because it has zero speed and is ...
There are two main descriptions of motion: dynamics and kinematics.Dynamics is general, since the momenta, forces and energy of the particles are taken into account. In this instance, sometimes the term dynamics refers to the differential equations that the system satisfies (e.g., Newton's second law or Euler–Lagrange equations), and sometimes to the solutions to those equations.
Disregarding loss or gain however, the sum of the kinetic and potential energy remains constant. Kinetic energy can be passed from one object to another. In the game of billiards, the player imposes kinetic energy on the cue ball by striking it with the cue stick. If the cue ball collides with another ball, it slows down dramatically, and the ...