For the structural systems below $($Figure $1($a$)$ and $($b$)),$ determine:

a$)$ Find the natural period of vibration for the conventional system.

b$)$ Find the natural period of vibration for the isolated system.

c$)$ Use the Design Spectra $($Figure $2)$ and determine the structure spectral acceleration

$($conventional and isolated structures$).$

d$)$ Considering the results from item $b,$ determine the maximum displacement $($conventional and

isolated structures$).$

e$)$ Considering the results form item b$,$ determine the maximum system base shear $($conventional

and isolated structures$).$

f$)$ Considering the results from item d$,$ determine the maximum system overturning moment

$($conventional and isolated structures$).$

Damping ratio $=2\%$ for conventional structure and $10\%$ for isolated structure;

Isolator transverse translational stiffness $=4200k\frac{N}{m}.$

Note: Consider that the bearing's vertical stiffness is infinitely rigid, and the bearing's rotational

and torsional stiffness are negligible.