Q$2$ The structures shown in Figure $2,$ is a roof slab supported by four columns of circular dimensions, of diameter $600mm.$ Assuming the load is concentrated in the stiff slab, determine:

$($a$)$ The natural frequency and Period, assuming motion is in the vertical direction

$($b$)$ The natural frequency and Period, assuming motion is in the horizontal direction

Density of Concrete, ${}_c=24k\frac{N}{m^3}$

Acceleration due to gravity, $g=9\mathrm{.}81\frac{m}{s^2}$

Dimensions, $l=6m,b=6m,h=12m$

Young's Modulus of Concrete, $E_c=35,000$MPa

Thickness of Slab, hc$=200mm$

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Figure $2$

Reinforced Concrete Structure