# SHM with friction

1. Nov 2, 2007

### SciencePF

Suppose a mass is oscillating attached to a spring in a horizontal surface with friction. Friction sooner or later will stop the oscillation. Does exists any possibility that the oscillating object stops at equilibrium position of that SHM, or it will stop elsewhere but never in the equilibrium position, i.e., x=0? TIA.

2. Nov 2, 2007

### muppet

It's certain to stop at the equilibrium position. The reason SHM happens is because there's a restoring force that acts to return the particle to that position; as the system loses energy it can no longer store energy in the potential creating that force (e.g. gravity in the case of the simple pendulum), so the amplitude of oscillation dies off.

3. Nov 2, 2007

### Meir Achuz

It need not stop at x=0 if there is static friction.
It will stop when the retarding kinetic friction force finally brings v to zero.
This could occur at x=0, as well as other x.

4. Nov 3, 2007

### SciencePF

The retarding kinetic friction force is constant, so as the oscillator slows down, there will be a moment that the restoring force has a shorter value than kinetic friction force, and this never occur at origin, so i suppose it cant never stops at x=0.

5. Nov 3, 2007

### muppet

If the frictional force exceeded the restoring force, the "oscillator" would never oscillate; when displaced by a small distance the frictional force would exceed the restoring force, and energy would stay stored in the stretched spring.
The force experienced by the particle isn't affected by its velocity; only by the spring constant and the instantaneous displacement; F=-kx.

6. Nov 3, 2007

### Staff: Mentor

Not necessarily. The position where it stops will depend on where it starts. If the damping force is constant then there are two positions from which the oscillator is started and will stop at the origin.

7. Nov 3, 2007

### SciencePF

Thanks to all who contribute to clarifying this question!

Astronuc:
What do you mean when you wrote this:
"If the damping force is constant then there are two positions from which the oscillator is started"

Thanks

8. Nov 3, 2007

### Staff: Mentor

There are two positions from equilibrium. For example, take a spring. The force could be tension or compression with a displace that is + or - from the equilibrium (zero displacement) point. In other words, there is a symmetry in SHM.

9. Nov 3, 2007

### SciencePF

For me is difficult to understand why it can reach x=0 with friction.
Let´s explain if i understood:
When oscillating with friction there will be a moment where $$\mu$$N=kx. and after that $$\mu$$N>kx, so for the same spring the heavier the object the longer from the origin it will stop, unless when $$\mu$$N=kx it has enough kinetic energy to dissipate and stop elsewhere, that can include point x=0! Is this interpretation correct?

10. Nov 3, 2007

### Staff: Mentor

11. Nov 4, 2007

### muppet

If this bit was right, there'd simply be no oscillation. That SHM has already started to occur is indicative that there is no such moment.

Remember that in SHM the energy contained by the system doesn't directly affect the force experienced by the particle. The particle doesn't stop because of frictional forces balancing the restoring force of the spring. That can happen, but then you don't get SHM.

What happens instead is that work is done against friction and energy is lost from the system. As the system loses energy, the mass has less energy to store as potential energy in the spring, so the amplitude of the oscillation dies off to zero.