Forces on a string

A string setup as in our physical realization for studying waves is plucked at its center. (See Figure 1, next page.) The mass of the string is $M=10^{-2}$ kg, its length is $L=1$ m, the applied tension is $\tau=100$ N, and the string can sustain a maximum tension of $T=\sqrt{T_x^2+T_y^2}=200$ N before breaking.

(a)

What is the maximum distance $y$ (indicated in the figure) by which the string can be plucked before breaking?

(b)

If the string is held in the plucked position with $y=0.1$ m and then released, what will be the initial acceleration of each point of the string with $0<x<L/2$? For each point with $L/2<x<L$?
Hint: Use the wave equation derived in class.
Note: You may find it fun to think about the acceleration of the chunk at $x=L/2$ and what this all means in terms of how the string will move once released! We will answer that question later when we have the general solution to the wave equation.