Mass Spring System: Find Natural Frequencies & Mode Shapes

AI Thread Summary
To find the natural frequencies and mode shapes of a mass spring system with equal masses, one must conduct a free body analysis of the two masses involved. The problem requires setting up force and acceleration equations for each mass, particularly focusing on the vertical displacement of mass m1 relative to mass m2. By analyzing the forces in the springs and determining the net vertical force, one can derive the displacement and acceleration of the masses. This leads to the formulation of a differential equation that describes the system's dynamics. Understanding these concepts is crucial for solving the problem effectively.
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Homework Statement


Obtain the expressions for the natural frequencies and mode shapes for the case where m1=m2=m.

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Homework Equations




The Attempt at a Solution



I apologise for not making an attempt, this is just unlike anything I've seen.

I'd appreciate if anyone could demystify this problem.
 
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Do the usual free body analysis and write the force/acceleration equations for each of the two masses.
 
Consider mass m1. If at some time t it is displaced vertically downward wrt m2 by an amount x1, what are the forces in the springs? What is ythe net vertical force on it? What is its displacement relative to the ground? What is its acceleration? What differential equation does that give you?
 

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