Question: 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

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?

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