Mass matters for standing waves on a string?

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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