Find the length of a bungie cord when it hangs vertically in a steady state if the initial densi

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Find the length of a bungie cord when it hangs vertically in a steady state if the initial density of the cord is $R(A, 0) = a(1 - \frac{A}{2l_0})$, $0 \le A \le l_0$, where $l_0$ is the initial length of the cord.