What is the Angular Frequency of Two Masses on a Spring?

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Homework Help Overview

The problem involves two masses attached to a spring, with the goal of calculating the angular frequency of their oscillation. The subject area pertains to mechanics and oscillatory motion.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the relationship between the two masses and the spring, questioning how to derive a single equation from the two separate equations provided. There is also consideration of the center of mass and how the masses move relative to it.

Discussion Status

The discussion is ongoing, with participants exploring different interpretations of the problem and suggesting approaches to unify the equations for both masses. Some guidance has been offered regarding the center of mass, but no consensus has been reached.

Contextual Notes

There is a mention of the need to clarify the equations and the relationship between the movements of the two masses, as well as a request for confirmation of the suggested approach.

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Homework Statement


We attach two blocks of masses m1 = 10 kg and m2 = 4 kg to either end of a spring of spring constant k = 4 N/m and set them into oscillation. Calculate the angular frequency ω of the oscillation

Homework Equations


M_{1}{x}^{..}=k(w-x)
M_{2}{w}^{..}=-k(w-x)

where x and w are the distance from equilibrium position of m1 and m2 respectively.

Attempt

Honestly, I have absolutely no idea. How does one start this?
 
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Notice that the right-hand sides depend only on w-x. Wouldn't it be nice if you had an equation where the left-hand side depended only on (d/dt)2(w-x)? How could you get such an equation?
 
What can one say about the center of mass? How does each move with respect to the CM?

Also use \ddot{x} for \ddot{x}
 
Are you suggesting I make one equation for both masses instead of two separate equations?

x_{cm}=\frac{{m_{1}x_{1}+m_{2}x_{2}}}{{\sum{m}}}

x_{1}=w, x_{2}=x
 
I know this thread is old, but I was wondering if someone could confirm the attempt suggested in the above post.
 

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