Answer the following descriptive questions.

a. In the interpolation of displacement of a finite element, \(u(x)=\sum N_{I}(x) u_{I}\), which one depends on time and which one depends on domain?

b. Explain the difference between the consistent mass and lumped mass matrix.

c. Will the natural frequency using lumped mass matrix be larger or smaller than the actual natural frequency? Explain why.

d. If the mass of the system increases, will the natural frequency increase or decrease?

e. If the stiffness of the system increases, will the natural frequency increase or decrease?

f. Explain the difference between the eigenvalue problem and the generalized eigenvalue problem.
g. Explain why the magnitude of mode shape is not important.
h. If a 1D bar is modeled using 10 bar elements, when both ends of the bar are free, what would be the lowest natural frequency of the bar?
i. If a numerical integration algorithm is conditionally stable, how should we choose the timestep size?
j. Explain what the method of mode superposition is.