$2\mathrm{.}58.$ Consider the base motion problem of Figure $2\mathrm{.}13.($a$)$ Compute the damping ratio needed to keep the displacement magnitude transmissibility less then $0\mathrm{.}50$ for a frequency ratio of $r=1\mathrm{.}5.($b$)$ What is the value of the force transmissibility ratio for this system?

$($a$)$

$($b$)$

Figure $2\mathrm{.}13($a$)$ Base$-$excitation problem models the motion of an object of mass $m$ as being excited by a prescribed harmonic displacement acting through the spring and damper. $($b$)$ A free$-$body diagram of the base motion problem in $($a$).$