What Is the Period of Oscillation for Two Masses Connected by a Spring?

[dowjonez]

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

 

[Astronuc]

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?

 

[dowjonez]

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.

 

[Ratzinger]

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.

 

[Ratzinger]

http://www.andrew.cmu.edu/course/33-231/coup-osc.pdf