Consider the boundary-value problem introduced in the construction of the mathematical model for the shape of a

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Consider the boundary-value problem introduced in the construction of the mathematical model for the shape of a rotating string:

+ poły = 0, y(0) = 0, y(L) = 0. %3D dx2


For constant T and ρ, define the critical speeds of angular rotation ωn as the values of v for which the boundary value problem has nontrivial solutions. Find the critical speeds ωn and the corresponding deflections yn(x).

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