Mass matters for standing waves on a string?

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The discussion centers on the dynamics of a massless string with a small ball of mass m attached to it. The equation of motion A cos(Wt) is analyzed, with terms defined to understand the system's behavior. There is uncertainty about whether the presence of the ball affects the string's motion. Participants are encouraged to present their best attempts at solving the problem for further assistance. The conversation highlights the importance of understanding the implications of mass in wave equations.
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)
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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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