Springs connected to a mass in series?

[flinnbella]

Yes, there are.

Doing the free body diagrams (FBD) for each component (the ceiling $c$, the spring $k_1$, the spring $k_2$ and the mass $m$):

View attachment 332141​

By definition, from one FBD to the next:
$$F_c = F_{k1}$$
$$F_{k1} = F_{k2}$$
$$F_{k2} = F_m$$
mass FBD:
$$F_m = mg$$
Therefore:
$$F_c = F_{k1} =F_{k2} = F_m = mg$$
The force $mg$ goes through every component.

No, that can't be right. F K1 would be directed upward, not downwards, because the spring will be stretched downwards, and so FK1 will apply a restoring force upwards.

 

[erobz]

No, that can't be right. F K1 would be directed upward, not downwards, because the spring will be stretched downwards, and so FK1 will apply a restoring force upwards.

On the thing that is attached to below ( i.e. spring 2 ) it is applying a restoring force $F_{k2}$, which is equal and opposite the force that is applied to spring 1. ($F_{k1} = - F_{k2}$)

 

[hutchphd]

The force mg goes through every component.

This is true but that means they all have magnitude mg but they are not all mutually action-reaction pairs. There are three such pairs but the others are known equal and opposite because each spring is not experiencing acceleration or deformation.

 

[erobz]

This is true but that means they all have magnitude mg but they are not all mutually action-reaction pairs. There are three such pairs but the others are known equal and opposite because each spring is not experiencing acceleration or deformation.

And in the case of the oscillator( which is @flinnbella original problem) the forces on opposite ends of each spring are equal and opposite because the springs are “massless”.

 

[hutchphd]

Yes I had forgotten the Original Post!

 

[erobz]

Yes I had forgotten the Original Post!

Yeah… we have been walking around a little bit in hopes to get a flag in the ground…somewhere.

 

[jack action]

No, that can't be right. F K1 would be directed upward, not downwards, because the spring will be stretched downwards, and so FK1 will apply a restoring force upwards.

Those are only the magnitudes. You can see the direction of the vectors on the drawing where I already assumed that the forces acting on each component are equal and opposite.