How Do You Model Forces in a Two Mass Spring System?

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SUMMARY

The discussion focuses on modeling forces in a two-mass spring system where mass 1 moves horizontally and mass 2 moves vertically, connected by a spring with constant k and rest length L. The primary forces acting on the masses include the spring force and gravitational force on mass 2. The participants express difficulty in deriving Newton's equations due to the complexity of the forces involved, particularly the changing direction of the spring force during oscillation, leading to the conclusion that the problem may be mathematically unsolvable without a clear geometric representation.

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  • Understanding of Newton's laws of motion
  • Knowledge of spring mechanics and Hooke's Law
  • Familiarity with gravitational force calculations
  • Basic concepts of oscillatory motion and equilibrium
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hurdler788
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I would love it if someone helped me out on this problem!

So, we have two identical masses. mass 1 can only move horizontally on a smooth surface, and mass two can only move vertically. These two masses are connected by a spring of constant k and the rest length of the spring is L. There is no friction. The spring is a directly connected, so it looks like the spring goes through the table, but it really doesnt...

I am looking for the forces on both blocks so I can write Newton's equations.

I know that they both have a spring force applied, and the vertical block has gravity... but that is where I get stuck.

Please help!
 
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For mass 1 and 2 weight is a force that acts. On mass 2 if only weight would act the block would pass through the table, so what can you conclude.
The other force would be the string force on each block as you pointed out.
 
I'm not sure this is solvable. My intuition says the mass hanging over the edge will simply pull the other one at least near the edge. Even if there was some anti-symetric mode that had maximum spring tension while the hanging mass was at it's lowest point, the direction of the spring force changes dramatically with oscilation, forbiding you from using the small-angle approx. Unless I'm not getting the setup, this seems like a mathematically impossible problem.
 
Is there a picture, or even a verbal description of the actual geometry of this problem? I cannot understanding it from what has been written here.
 

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