TooFastTim said:Just reading up on lagrangeans and I came across an expression for potential energy I'd never seen before: V=(1/2)*m*w2*x2.
Energy in a spring E=(1/2)kx^2
w=SQRT(k/m)
k = w^2m
E=(1/2)m(w^2)(x^2)
Yep. Simple harmonic oscilaror.
m = mass
w = angular frequency
x = maximum displacement / amplitude
The expression gives the total energy only when the kinetic energy vanishes, at the turning points. Damping is irrelevant to the issue. Even if damping is present, the expression still gives the total mechanical energy of the harmoic oscillator when and only when the kinetic energy vanishes, at the turning points. In general, the expression does not give the total energy.Dadface said:There is a continual interchange between PE and KE and the equation does give the total energy(ignoring damping).
turin said:The expression gives the total energy only when the kinetic energy vanishes, at the turning points. Damping is irrelevant to the issue. Even if damping is present, the expression still gives the total mechanical energy of the harmoic oscillator when and only when the kinetic energy vanishes, at the turning points. In general, the expression does not give the total energy.
Potential energy is the energy possessed by an object due to its position or configuration. It is a form of stored energy that can be converted into other forms, such as kinetic energy.
The formula for potential energy is PE = mgh, where m is the mass of the object, g is the acceleration due to gravity, and h is the height of the object. Alternatively, for objects with a spring-like potential, the formula is PE = (1/2)*k*x^2, where k is the spring constant and x is the displacement from equilibrium.
Potential energy and kinetic energy are two forms of energy that are interchangeable. When an object gains potential energy, it loses kinetic energy, and vice versa. This is known as the law of conservation of energy.
This formula is used to calculate the potential energy of an object with a spring-like potential, where V is the potential energy, m is the mass of the object, w is the angular frequency of the oscillation, and x is the amplitude of the oscillation.
Some examples of potential energy include a ball at the top of a hill, a stretched rubber band, a compressed spring, and a pendulum at its highest point. In each of these cases, the object has the potential to do work because of its position or configuration.