A ball of mass M is suspended from a string of length l which has a finite mass

Question

A ball of mass M is suspended from a string of length l which has a finite mass m. Consider small oscillations on the string.
What is general solution y(x,y) for the standing waves on the string?
What are the boundary conditions on y(x,y) at x=0 x=l ?
What is the equation of the normal modes on the string ? Sketch both side of the equation and indicate graphically the solutions.
Show that for M>>m the frequency of the slowest normal mode is equal to the frequency of the pendulum with massless string of length l.

Explanation / Answer

y(x,t)=Asin(t+kx+)

y(0,0)=0

y(l,t)=0

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