Two masses attached with a spring.

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SUMMARY

The discussion focuses on a mechanical system consisting of two masses, M1 and M2, connected by a massless spring with a force constant k and an unstretched length a. Participants seek to derive the normal coordinates and normal frequencies of vibration for the system. The initial steps involve formulating the equations of motion for each mass, despite uncertainties regarding the boundary conditions and definitions of "normal coordinates." The conversation emphasizes the importance of understanding the system's constraints and the fundamental principles of oscillatory motion.

PREREQUISITES
  • Understanding of classical mechanics, specifically oscillatory motion
  • Familiarity with spring dynamics and Hooke's Law
  • Knowledge of normal modes and normal frequencies in mechanical systems
  • Basic mathematical skills for solving differential equations
NEXT STEPS
  • Study the derivation of equations of motion for coupled oscillators
  • Learn about normal mode analysis in mechanical systems
  • Explore the concept of normal coordinates in multi-body systems
  • Investigate the application of differential equations in mechanical vibrations
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Physics students, mechanical engineers, and anyone interested in the dynamics of oscillatory systems will benefit from this discussion.

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1. Two masses M1 and M2 are joined by a massless spring of force constant k and unstretched length a. Obtain the normal coordinates of the system for motion along the line joining the particles, as well as the normal frequencies of vibration.http://tinypic.com/view.php?pic=33voh6v&s=7

Here is the picture given with the problem, it includes x distances from the wall. I'm not totally sure if the mass m1 is connected to the wall, or resting on a floor, as it doesn't say anything about that in the problem.

I'm not totally sure what "normal coordinates" are either. I'm just assuming the masses are only attached to each other, not the wall, and that "normal coordinates" is another way of saying "find the position/x value", which would explain the given x's.

Thank you!
 
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To begin with...

first, write down the basic equation for the motion of the particles individually!

What do u get??
 
I don't understand. The problem doesn't say anything about a force being applied to the spring system.
 

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