# Harmonic oscillator with/without gravity

#### daudaudaudau

If I have mass on a spring that is oscillating in a linear motion, this system has a certain energy. Now if we imagine the system to be aligned along the vertical, why is the energy lower when gravity is turned on? I can calculate it and see that it is correct, but what is the "explanation" ? Because, I mean, when gravity is turned on, the string is stretched further, so this should increase the energy.

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#### Doc Al

Mentor
When the system is vertical, you must also consider gravitational PE along with spring PE. Compare the increase in spring energy (as it stretches to the new equilibrium point, say) with the decrease in gravitational PE.

#### daudaudaudau

Right, and I can see that the decrease in gravitational PE is larger than the increase in the spring PE. Is there some general "law" stating that whenever you apply an external conservative force to a system, the energy decreases?

#### Doc Al

Mentor
Right, and I can see that the decrease in gravitational PE is larger than the increase in the spring PE.
That's only true if you compare the change in gravitational and spring PE as the masses lowers to its new equilibrium position. Since the gravitational force is constant, the spring force will soon overtake it. I don't see anything particularly significant about this. With respect to its new equilibrium point, a vertical spring+mass behaves similarly to a horizontal one.
Is there some general "law" stating that whenever you apply an external conservative force to a system, the energy decreases?
Not that I'm aware of.

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