Consider a mass m confined to the x axis and subject to a force F(adsbygoogle = window.adsbygoogle || []).push({}); _{x}=kx where k>0.

Write down and sketch the potential energy U(x) and describe the possible motions of the mass. (Distinguish between the cases that E>0 and E<0.

It is the part in parenthesis that confuses me. I can't picture what a negative value of energy would be.

I know the potential is U(x) = (1/2)kx^{2}, and that Total energy is kinetic plus potential (E = T + U). I also assume that the potential is always positive. If this is true, then the only was for the energy to be negative is to have the kinetic be negative and larger than the potential.

Does this refer to the case when the mass is moving in the -x direction giving T = -(1/2)mv^{2}?

It seems to me that the motion should be the same whether the energy is negative or positive since this is a classical mass and confined to the parabolic potential well. It seems like it should oscillate back and forth for any energy.

For some reason I don't think I am picturing this correctly.

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# Motion of a mass m confined to the x-axis (Hamiltonian)

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