A high$-$precision surveillance camera is placed on top of an isolator to prevent vibration of the recording. The camera has a mass of $5$ kg $,$ and the isolating base a stiffness of $18000\frac{N}{m}$ and a viscous damping constant of $80N-\frac{s}{m}.$ The camera's mounting surface experiences a harmonic disturbance caused by an unbalanced engine nearby $y(t)=$Ysin$(t),$ with the disturbance frequency measured at $=100ra\frac{d}{s}.$

Ysin$t$

Determine the maximum allowable floor displacement amplitude to limit the camera's vibration amplitude to $0\mathrm{.}5$ mm $.$

$0\mathrm{.}84$ mm

$1\mathrm{.}01$ mm

$0\mathrm{.}73$ mm

$1\mathrm{.}8$ mm