Please help with this Harmonic Motion

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SUMMARY

The discussion focuses on calculating the frequency of oscillatory motion for a system consisting of two masses (m1 = 100 g and m2 = 100 g) connected by a spring with a force constant (k = 0.5 N/m) on a frictionless track. The key insight is that the system's center of mass remains stationary, allowing each mass to oscillate independently. The effective spring constant for the system is halved, leading to the formula for angular frequency ω = sqrt(k/(m1 + m2)). The frequency of oscillation can then be derived from this angular frequency.

PREREQUISITES
  • Understanding of harmonic motion principles
  • Familiarity with spring constants and their effects on oscillation
  • Knowledge of center-of-mass concepts
  • Basic calculus for deriving frequency from angular frequency
NEXT STEPS
  • Calculate the frequency of oscillation using the formula f = ω/(2π)
  • Explore the concept of effective spring constants in multi-mass systems
  • Study the implications of center-of-mass in oscillatory motion
  • Investigate the effects of damping on harmonic motion
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Please help with this! Harmonic Motion

Two masses m1=100 g and m2=100 g slide freely in a horizontal frictionless track and are connected by a spring whose force constant is k=.5 N/m. Find the frequency of oscillatory motion for this system. I know omega = sqrt (k/m), but I have two masses, rather than just one. How does this work? Could someone give me an idea of how I should go about solving this?

Thanks!
 
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there's a place in the spring which doesn't move (the center-of-mass).
so each side of the spring stretches independently, with a new k.
 

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