What is Potential Energy? Learn About V=(1/2)*m*w2*x2

[TooFastTim]

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.

I suppose all you physics majors are familiar with it. But what is it and where can I find out more?

 

[Dadface]

This looks like the equation giving the total energy of a system that moves with simple harmonic motion.

 

[flatmaster]

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

 

[turin]

It it not the total energy, it is, as the OP suggests, the potential energy. The total energy of the harmonic oscillator must also include the kinetic energy.

 

[Dadface]

There is a continual interchange between PE and KE and the equation does give the total energy(ignoring damping).Expressing it another way it gives the maximum KE(when PE is zero) or the maximum PE(when KE is zero)

 

[turin]

There is a continual interchange between PE and KE and the equation does give the total energy(ignoring damping).

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]

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.

Think of a simple pendulum,at the ends of the swing the bob has PE only and at the bottom it has KE only.At any other position it has a mixture of the two and if damping is negligible the PE plus KE remains constant.Similar reasoning can be applied to any other system that moves with SHM.

 

[TooFastTim]

Thanks guys.