For the two-story shear building shown in Problem 9.5:
(a) Determine the natural vibration frequencies and modes; express the frequencies in terms of m, , and h.
(b) Verify that the modes satisfy the orthogonality properties.
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(c) Normalize each mode so that the roof displacement is unity. Sketch the modes and identify the associated natural frequencies.
(d) Normalize each mode so that the modal mass Mn has unit value. Compare these modes with those obtained in part (c) and comment on the differences.
Using the definition of stiffness and mass influence coefficients, formulate the equations of motion for the two-story shear frame with lumped masses shown in Fig. P9.5. The beams are rigid and the flexural rigidity of the columns is . Neglect axial deformations in all elements.