An accelerometer with mass \(=0.01 \mathrm{~kg}\) and a damping ratio \(=\) 0.707 is to be designed. What should be the undamped natural frequency of the system so that the measurement error never exceeds \(2 \%\) ? The vibration signal, which is to be measured, can have a frequency as high as \(200 \mathrm{~Hz}\).

Corroborate the validity of your design using MATLAB ODE23 or ODE45 for the signal frequency \(=80 \mathrm{~Hz}\). Show the signal that your instrument will produce after it has been attached to the vibrating structure.