Find the modal frequencies and mode shapes for the frame

Question

m₁ = 0.70 kip.sec²/ft I₁ = 300 in⁴
m₂ - 0.70 kip.sec²/ft I₂ 300 in*
m₃- 0.65 kip. sec²/ft I₃ - 280 in⁴
m₄ - 0.55 kip sec²/ft I₄ - 280 in⁴

All columns have E = 29,030 ksi and L = 13 ft.

• Find the modal frequencies and mode shapes for the frame assuming the columns are fixed at the top and the bottom (i.t , the floors are rigid enough to inhibit rotation).
• Sketch out the first and third mode shape. Next to each mode shape, write the period for that mode.
• If you relaxed the assumption that the columns were rigidly fixed at the top and bottom, would the modal frequencies increase or decrease? Explain.