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**2 Masses 1 Spring Question! Help**

## Homework Statement

Two masses m1 and m2 slide freely on a frictionless horizontal plane, and are

connected by a spring of force constant k . Find the natural frequency of oscillation for

this system.

## Homework Equations

[tex] \ddot{x} + \omega^2x=0 [/tex] where [tex]\omega^2 = \frac{k}{m}[/tex]

[tex] \nu = \frac{\omega}{2\pi} [/tex]

## The Attempt at a Solution

So I had no clue where to start with this question so I asked the prof and he told me you don't have to used reduced mass or center of mass for this question. He said just to consider the equations of motion for both masses.

Alright so let's say m1 is displaced by a distance x to the left then

[tex] \ddot{x} + \frac{k}{m1}x = 0 [/tex]

Now I'm not sure if this is right, but m2 also feels a stretch in spring by displacement x but the force is in opposite direction of m1 so:

[tex] \ddot{x} - \frac{k}{m2}x = 0 [/tex]

Now what do I do with both these equations? I'm lost someone please help guide me along here! Thanks