A circular bar with a length of \(80 \mathrm{~cm}\) and radius of \(3 \mathrm{~cm}\) is made of steel which has an elastic modulus \(200 \times 10^{9} \mathrm{~N} / \mathrm{m}^{2}\) and mass density \(7600 \mathrm{~kg} / \mathrm{m}^{3}\). The bar has a mode shape of \(X(x)=33.91 \cos 13.74 \mathrm{x}\).

(a) Determine the potential energy of this mode.

(b) Determine the kinetic energy of this mode.

(c) What is the natural frequency that corresponds to this mode?