E.P.E. -> ? when 2 masses are attached to a spring

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SUMMARY

When two masses, m and M, are attached to a compressed spring, the elastic potential energy converts into kinetic energy upon decompression. The center of mass remains at rest while the masses oscillate around it. The effective total mass is calculated using the formula 1/Mt = 1/M1 + 1/M2, which influences the system's frequency in conjunction with the spring stiffness. The kinetic energy distribution between the masses occurs in inverse proportion to their respective masses.

PREREQUISITES
  • Understanding of elastic potential energy and kinetic energy conversion
  • Familiarity with the principles of conservation of momentum
  • Knowledge of center of mass calculations
  • Basic concepts of oscillatory motion and resonance
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  • Study the principles of conservation of energy in mechanical systems
  • Learn about the calculation of effective mass in series systems
  • Explore the dynamics of oscillatory systems and resonance frequency
  • Investigate the relationship between mass distribution and kinetic energy sharing
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Two masses m and M are attached to a compressed spring. When the spring decompresses, the masses won't be pushed off the spring. What will happen to the masses and the entire system? By conservation of energy, the elastic potential energy of the spring will convert into kinetic energy, but which mass / entire system will have an increase in K.E.? What will happen to the center of mass?
 
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You should consider not only energy but momentum conservation. The center of mass keeps at rest. The masses oscillate around it.
 
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I think it may be analogous to a capacitor with two inductors connected across it. This system has only one resonance, caused by the combined inductance. So the combined masses will determine the frequency, in combination with the spring stiffness. As the masses act in series, we need to find the effective total mass from 1/Mt = 1/M1 + 1/M2. The kinetic energy is entirely in the motion of the masses and would seem to be shared in inverse proportion to the masses.
 

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