# Does a perfect spring oscillate forever in gravity?

• albertrichardf
In summary, we discussed the behavior of a perfect spring without friction or elastic limit and how it would react to being turned vertically in Earth's gravitational field. We also explored the concept of perpetual oscillation and how it is affected by friction and perturbations from the environment in real-world systems. This has applications in the design of sensitive and precision equipment.
albertrichardf
Suppose you have a perfect spring. By that I mean a spring that experiences no friction whatsoever, even internal, and that there is no elastic limit. Thus it obeys Hooke's law perfectly. Its own weight is negligible, and there is a point mass attached to the end of the spring.
Now, the spring is held horizontally at first in Earth's gravitational field and is turned vertically suddenly. Gravity will exert a force on the spring, and the spring will extend, till the point where its own force balances that of gravity, shifting the equilibrium point of the spring.
However, in reaching its new equilibrium point, the spring must have picked up velocity from gravity. While the force at equilibrium is zero, the velocity is not, and the spring should continue oscillating as if it were disturbed from equilibrium.
My question is if this oscillation is constant. Will the spring continue oscillating forever with the same amplitude?
Also, if this is the case, is friction in the spring and the surroundings the reasons why this is not observed? Or is it just one source of friction?

Albertrichardf said:
My question is if this oscillation is constant. Will the spring continue oscillating forever with the same amplitude
Yes. You can get this result from conservation of energy.
Also, if this is the case, is friction in the spring and the surroundings the reasons why this is not observed? Or is it just one source of friction?
Well, "the surroundings" means "outside the spring", and between that and inside the spring, there's nowhere else to look for other sources of friction.

albertrichardf

@Albertrichardf

If you observed the motion of an imperfect suspension spring and mass system in a real world environment and over a long period what might you expect to see ?

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I would expect an initial oscillation, that would eventually decay.

The motion never actually comes to a complete stop - why do you think that is ?

Nidum said:
The motion never actually comes to a complete stop - why do you think that is ?
You mean the spring continues oscillating forever? Is that actually the case? Because I would have though that the friction would dissipate energy from the spring, hence reducing the amplitude till the amplitude becomes zero. I actually don't see how the spring could be in motion.

Nidum said:
The motion never actually comes to a complete stop - why do you think that is ?
When we model the spring as an ideal spring that loses a fraction of its energy on each oscillation, you're right - we get a differential equation that says that the motion never stops completely. However, that model breaks down as the energy of each oscillation becomes smaller and approaches the random thermal energy of the atoms making up the spring. Real non-ideal springs do stop oscillating eventually.

@Nugatory

What I was encouraging @Albertrichardf to think about was what happens to the motion of a real spring mass system in a real environment .

Perturbations from the environment are usually sufficient to sustain small amplitude motion of any mechanical system which is capable of oscillation and which is not heavily damped or actively controlled in some way .

Usually the perturbations come from sources like air currents , ground movements , thermal expansion or stray magnetic fields .

With a real spring mass system the large scale oscillation will usually die away quite quickly but there is always going to be some residual component of oscillation maintained by these perturbations . At this small scale of movement the actual motion is often complex and continually mutating from one mode to another .

Study of this problem has application in the design of sensitive and/or precision equipment .

All right. Thanks for the answers. I was talking about large-scale oscillations though, those that are readily visible to the naked eye. It is interesting though to find out about smaller-scale perturbations from the environment.

## 1. What is a perfect spring?

A perfect spring is a hypothetical spring that follows Hooke's law, which states that the force exerted by the spring is directly proportional to its displacement from its equilibrium position.

## 2. What is oscillation?

Oscillation is the repetitive back and forth movement of an object between two points. In the case of a spring, it refers to the motion of the spring as it stretches and compresses.

## 3. Why is gravity a factor in the oscillation of a spring?

Gravity is a factor because it affects the weight of the spring and any object attached to it, causing it to stretch and compress at a certain rate. It also determines the equilibrium position of the spring.

## 4. Does a perfect spring oscillate forever in gravity?

No, a perfect spring will not oscillate forever in gravity. Due to the presence of friction and air resistance, the energy of the spring will gradually dissipate and the oscillations will eventually come to a stop.

## 5. What factors affect the oscillation of a spring?

The factors that affect the oscillation of a spring include the mass attached to the spring, the stiffness of the spring, the amplitude of the oscillations, and external forces such as gravity, friction, and air resistance.

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