2 masses connected by spring

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In summary, the conversation discusses how to find the period of oscillation for a system of two masses connected by a spring with a spring constant k. The equilibrium positions of the masses are x1 = 0 and x2 = 0, and the problem is complicated by the fact that the center of mass can move. The x1 and x2 coordinates refer to the displacement of the masses, and the system's mode of motion is a stretching mode. Resources for solving this problem include searching for coupled harmonic oscillators or normal modes on the internet.
  • #1
dowjonez
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consider two different masses m1 and m2. They are connected together by a spring. Assuming the spring has a spring constant k. Assume the equilibrium positions are x1= 0 and x2 = 0. Find the period of oscillation.


I know the the angular frequency is a function of both masses not just one mass like a fixed system.


im really stuck on this one
 
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  • #2
Yep, this is a tricky problem because nothing is fixed and the center of mass can moved. However, at equilibrium, the spring length is given by the difference in the equilibrium positions of both masses.

Are you sure about x1 = 0 and x2 = 0?
 
  • #3
yes that's what it says in the question. I am thinking that the x1 and x2 coordinates must be the displacement. So at time 0 neither are displaced. Also it was given that the mode of motion for the system was a stretching mode.
 
  • #4
Since this a very important piece of physics I'm sure there is plenty on the internet.

Just goggle coupled harmonic osciallators or normal modes.
 

1. How does a spring affect the motion of two masses connected by it?

A spring affects the motion of two masses by exerting a force on both masses in the direction of its equilibrium position. This force causes the masses to oscillate back and forth around the equilibrium point.

2. What factors affect the period of oscillation for two masses connected by a spring?

The period of oscillation is affected by the mass of the masses, the spring constant, and the amplitude of the oscillation. As the mass or spring constant increases, the period of oscillation increases. However, as the amplitude increases, the period of oscillation decreases.

3. How does the spring constant affect the force exerted on the two masses?

The spring constant is a measure of the stiffness of the spring and is directly proportional to the force exerted on the masses. As the spring constant increases, the force exerted on the masses also increases.

4. What is the relationship between the displacement of the masses and the force exerted by the spring?

The displacement of the masses from the equilibrium position is directly proportional to the force exerted by the spring. This means that the farther the masses are from the equilibrium point, the greater the force exerted by the spring will be.

5. How does the energy change in a system of two masses connected by a spring?

In a system of two masses connected by a spring, energy is constantly being exchanged between potential energy and kinetic energy as the masses oscillate back and forth. At the equilibrium point, all of the energy is in the form of potential energy, while at the maximum displacement, all of the energy is in the form of kinetic energy.

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