Acceleration of a spring - mass system

[songoku]

Yes, but what "constant speed"?

hhmm... I think the value of the speed will be zero because initially object 1 to 3 does not move and no acceleration means that no resultant force acting on it.

So, at the instant the wire is cut, only object 4 will move?

Thanks

 

[haruspex]

hhmm... I think the value of the speed will be zero because initially object 1 to 3 does not move and no acceleration means that no resultant force acting on it.

So, at the instant the wire is cut, only object 4 will move?

Thanks

Yes.

 

[songoku]

Yes.

What if I modify the question a little bit, find the acceleration 2 seconds after the wire is cut?

This is what I have in my mind:
The m₄ will push the right spring so the new extension (x₃) will be less than x₂ and all the other masses will move.

The extension on left spring does not change (still x₁) because the left spring, m₁ and m₂ will move as one system so the acceleration of m₁ and m₂ will be the same.

This means that the left spring will behave just like an inelastic string.

The magnitude of a₁, a₂ and a₃ will always be the same but all the acceleration, including a₄ won't be constant because there is continuous change in the extension of right spring, therefore there is continuous change in restoring force and there is continuous change in resultant force.

Am I correct?

If yes, how to set up equation of m₄ to account for continuous change in acceleration?

Thanks

 

[haruspex]

What if I modify the question a little bit, find the acceleration 2 seconds after the wire is cut?

Then you will need to have unknowns for the positions of three of the four masses independently (m1 and m3 will have a fixed relationship) and write the differential equations relating them. It is safe to assume there will be SHM involved, but it might be quite complicated.

 

[songoku]

Then you will need to have unknowns for the positions of three of the four masses independently (m1 and m3 will have a fixed relationship) and write the differential equations relating them. It is safe to assume there will be SHM involved, but it might be quite complicated.

Ok then I will leave it for now

Thank you very much for all the help BvU, haruspex, vela