A beam with a length \(L\) cross-sectional area \(A\), and moment of inertia \(I\) is made of a material with an elastic modulus \(E\) and mass density \(ho\) and has a normalized transverse mode shape \(X_{k}(x)\) which corresponds to a natural frequency \(\omega_{k}\).

(a) What is the potential energy of a system that vibrates with this mode shape?

(b) What is the kinetic energy of a system that vibrates with this mode shape?