Free body diagram for mass on oscillating spring

[physics20]

Homework Statement

What does the free body diagram look like for a mass on an oscillating spring, when the mass is at its midpoint.

Homework Equations

F=-kx

The Attempt at a Solution

I'm not sure how an oscillating spring FBD is different from one for a non-oscillating spring. I don't know what to include other than an upward directed spring force and a downward directed weight force.

Also, For a mass on spring with a mass m and spring constant k (if the mass was not oscillating the spring would be extended a length L), what is the directions and relative magnitudes of the accelerations at the bottom and at the midpoint?

 

[cepheid]

Welcome to PF!

Remember that the spring restoring force depends upon the displacement from the equilibrium position. So, if the mass is oscillating, the force will vary depending upon where in the oscillation the mass is. If it is at that midpoint, this IS the spring's equilibrium position. Hence, the displacement from the equilibrium position (x) equals 0. So...is there any spring restoring force acting at that position?

 

[physics20]

No there isn't. So does that mean that the free body diagram at the midpoint would only have the downward force of the weight of the mass?

And would that also mean that the acceleration of the mass when it is at the midpoint is 0 (because acceleration is also dependent on the displacement)?

 

[cepheid]

Hmmm...well if it's a vertical system, then I guess the definition of "equilibrium position" changes. The midpoint of the oscillation will be the point at which all the forces are balanced (and hence the acceleration is indeed zero). This point will occur not when the spring is completely unextended or uncompressed, but rather when the spring is extended just enough that the restoring force balances the weight. So I was not quite correct above.

 

[physics20]

Ok that makes sense, except I'm still confused about what forces to include on the free body diagram for the mass when its at the midpoint. Is it just the weight force, or is there a spring force that I also have to account for?

 

[cepheid]

Ok that makes sense, except I'm still confused about what forces to include on the free body diagram for the mass when its at the midpoint. Is it just the weight force, or is there a spring force that I also have to account for?

I answered this question in my previous post. At the midpoint, the system is in equilibrium, meaning that all forces are balanced. I said that.