The deck carries a uniformly distributed mass mr $=100$ kgm$-1$ and has vertical stiffness kr $=245$ kNm$-1.$ The stiffness of the wall and columns that contribute to withstand the vertical motion of mr are respectively kw $=2\mathrm{.}5$x$106$ kNm$-1$ and kc $=1/10$ kw$.$ The span is $50$m

Develop a model based on masses and springs to investigate vertical vibrations of the roofing system. To represent the deck, use as many as $3$ lumped masses equally spaced along the span. Assume that the stiffness of each segment of the deck, in$-$between lumped masses, equals $4$kr and that the extreme deck segments firmly attach to the supporting wall or column.

Determine the corresponding modal shapes.