PROBLEM

A SDOF portal frame fixed at its base has a mass

of $2500$ kg at roof level. Lateral stiffness of frame

columns on one side is $16,000\frac{N}{m}$ and the other side

is $13,000\frac{N}{m}$ and viscous damping coefficient is $750$

$N-\frac{s}{m}.$ Under free vibrations, find the natural period of

oscillations and cyclic as well as circular natural

frequencies for both damped and undamped

conditions. For the damped condition, if the initial

displacement and velocity are $20$ mm and $25\frac{mm}{s}.$

respectively, compute frame side sway after $1\mathrm{.}9$ s $.$