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

In summary, the conversation discusses a problem involving two identical masses connected by a spring, where one mass can only move horizontally and the other can only move vertically on a smooth surface with no friction. The speaker is looking for the forces on the blocks in order to write Newton's equations, and mentions the spring force and gravity as possible forces. However, it is unclear how the problem is set up and it may be mathematically impossible to solve.
  • #1
hurdler788
2
0
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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  • #2
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.
 
  • #3
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.
 
  • #4
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.
 

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

1. How do you determine the equations of motion for a two mass spring system?

To determine the equations of motion for a two mass spring system, you will need to use Newton's Second Law of Motion and apply it to each mass individually. This will result in two second-order differential equations, which can be solved using various methods such as the Laplace transform or the method of undetermined coefficients.

2. What are the boundary conditions for a two mass spring system?

The boundary conditions for a two mass spring system are the initial conditions, such as the initial positions and velocities of the masses, as well as the boundary conditions at the interface between the masses, such as the stiffness and damping coefficients of the springs connecting them.

3. How do you solve for the natural frequencies and mode shapes of a two mass spring system?

To solve for the natural frequencies and mode shapes of a two mass spring system, you will need to solve the characteristic equation of the system, which is obtained by setting the determinant of the coefficient matrix to zero. The natural frequencies and corresponding mode shapes can then be determined from the roots of the characteristic equation.

4. Can you determine the stability of a two mass spring system?

Yes, the stability of a two mass spring system can be determined by analyzing the eigenvalues of the coefficient matrix. If all eigenvalues have negative real parts, the system is stable. If any eigenvalue has a positive real part, the system is unstable.

5. Are there any simplifying assumptions that can be made when solving a two mass spring system?

Yes, depending on the specific problem at hand, simplifying assumptions such as negligible damping or small displacements may be made to simplify the equations of motion and make them easier to solve. However, these assumptions may not always accurately represent the real-world behavior of the system.

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