Understanding Coupled Oscillators: Solving for Forces on Two Masses

In summary, the problem involves two masses attached to two springs with identical spring constants and masses. The equations of the forces on the masses are F_1 = -kx_1 + k(x_2 - x_1) and F_2 = kx_1 - kx_2, where x_1 and x_2 represent the displacements of the masses. The masses start at position zero and are then moved to the right. It is important to consider unstretched lengths to prevent the masses from colliding with each other or the wall.
  • #1
Tuneman
41
0
Ok here's the problemo:

|
|ooooo[m1]00000[m2]
| I have two masses attached to two springs, the "ooo"s are the springs, and the "[m]"s are the masses, the spring constants are the same , and so are the masses. I know to do the problem, the only thing is I am having trouble figuring out the equations of the forces on the two masses.I thought [tex] F_1 = -kx_1 + k(x_2 - x_1) , F_2 = kx_1 - kx_2 [/tex]

where [tex] x_1 [/tex] is the displacement to the right from [tex] m_1 [/tex] and [tex] x_2 [/tex] is the displacement to the right from [tex] m_2 [/tex]
 
Last edited:
Physics news on Phys.org
  • #2
You probably need some unstretched lengths in there somewhere otherwise your masses are going to be beating against the wall and each other.
 
  • #3
Well they are at position zero as they appear in the picture and then they are moved to the right
 
  • #4
Ah, ok, that works too. Looks like you have it right then.
 

1. What are coupled oscillators?

Coupled oscillators are a system of two or more oscillating bodies that are connected by a spring or some other form of coupling. These oscillators interact with each other and can affect each other's motion.

2. How do you solve for forces on two masses in a coupled oscillator system?

To solve for forces on two masses in a coupled oscillator system, you can use the equations of motion for each individual mass and the equation for the coupling between them. This will allow you to determine the net force on each mass and how they are affected by the coupling.

3. What is the significance of the natural frequency in a coupled oscillator system?

The natural frequency is the frequency at which an oscillator naturally vibrates without any external forces. In a coupled oscillator system, the natural frequency of each individual oscillator can affect the overall behavior of the system and how they interact with each other.

4. How does damping affect the motion of coupled oscillators?

Damping is the process of reducing the amplitude of an oscillator's motion over time. In a coupled oscillator system, damping can affect the amplitude and frequency of the oscillators, which can in turn affect their interaction and the forces on each mass.

5. Can coupled oscillators exhibit resonance?

Yes, coupled oscillators can exhibit resonance when the natural frequencies of the individual oscillators are close to each other. This can result in a large amplitude of motion and can have important implications in various fields such as engineering and physics.

Similar threads

  • Advanced Physics Homework Help
Replies
9
Views
3K
  • Introductory Physics Homework Help
Replies
4
Views
684
Replies
7
Views
578
Replies
5
Views
310
  • Advanced Physics Homework Help
Replies
24
Views
6K
  • Advanced Physics Homework Help
Replies
4
Views
2K
Replies
3
Views
958
  • Introductory Physics Homework Help
Replies
3
Views
1K
  • Classical Physics
Replies
7
Views
1K
  • Advanced Physics Homework Help
Replies
9
Views
3K
Back
Top