Determine the natural frequencies, natural modes, and modal damping ratios for the two-story frame of Figure P9.5, with a damper only in the first story with damping coefficient  = 0.4 , where k =...

Determine the natural frequencies, natural modes, and modal damping ratios for the two-story frame of Figure P9.5, with a damper only in the first story with damping coefficient
 = 0.4
, where k = 24EI/
 is the story stiffness; express frequencies in terms of m and k. Show that the natural modes satisfy the orthogonality properties.