Mass matters for standing waves on a string?

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SUMMARY

The discussion centers on the dynamics of standing waves on a string with a massless string and a small ball of mass m attached at its midpoint. The equation of motion is represented as A cos(Wt), where A denotes amplitude and W represents angular frequency. The contributor assumes the string's mass equals that of the ball, raising questions about the impact of the ball's mass on the wave behavior. Clarification on these assumptions is essential for accurate analysis.

PREREQUISITES
  • Understanding of wave mechanics and standing waves
  • Familiarity with the equation of motion in physics
  • Knowledge of mass distribution effects in oscillatory systems
  • Basic grasp of angular frequency and amplitude in wave equations
NEXT STEPS
  • Study the effects of mass distribution on standing waves in strings
  • Explore the derivation of wave equations for systems with attached masses
  • Investigate the role of boundary conditions in wave motion
  • Learn about the principles of oscillation and resonance in physical systems
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Students of physics, educators teaching wave mechanics, and anyone interested in the dynamics of oscillatory systems involving mass and tension.

zooch
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Homework Statement
Does the equation of motion of a standing wave get impacted when a mass is attached to the string?
Relevant Equations
y = A cos(Wt)
1635094872486.jpeg


The question is to explain the equation of motion of the red ball. The string is massless and a small ball of mass m is attached to the string halfway. I just assumed the mass of the string is the same as the mass of the ball and explained the equation A cos(Wt) by defining the terms. I'm not sure if the small ball changes anything...
 
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