$20\mathrm{.}2$ An SDOF frame structure such as the one shown in Fig. $20\mathrm{.}3$ has a period of $0\mathrm{.}8$ sec and a damping factor of $2\%.$ The mass is $m=10lb-s\frac{e{c}^2}{in}.($a$)$ Using Fig. $20\mathrm{.}5,$ determine the value of the spectral velocity $S_v$ that applies to this structure. $($b$)$ Determine the corresponding values of $S_a$ and $S_d.($c$)$ Determine the maximum displacement of the mass. $($d$)$ Determine the maximum spring force.

Figure $20\mathrm{.}3$ SDOF system subject motion.