An instrument with mass \(=13 \mathrm{~kg}\) is to be isolated from aircraft engine vibrations ranging from 18,00 to \(2,300 \mathrm{cpm}\). What should be the stiffness of an isolator for at least \(65 \%\) isolation? Assume that the damping ratio is 0.045 .

Assuming that the initial conditions are zero, demonstrate the performance of your isolator for both the extreme frequencies \((1,800\) and 2,300 cpm) using the MATLAB routine ODE23 or ODE45. For each frequency, plot displacements of the radio and the support in a single figure. Then, also verify the analytical expression of the phase of the steady state response of the instrument.