An unbalanced engine mounted on an elastic support imposes a periodic vertical force on the support at the rotational frequency of the

engine. In order to determine the relationship between the engine rotational frequency and the resonance frequency of the elastically

supported engine, the engine run speed was slowly increased from its normal value of $500$ rpm to $600$ rpm $,$ which resulted in a trebling of

the amplitude of the measured displacement. No resonance was observed in the displacement response in the range of speeds

investigated.

Assuming that the damping present in the existing elastic support is negligible, determine:

The natural frequency of the elastically supported engine

rad$/$s$.$

Your answer should be acurate to $\frac{+}{-}0\mathrm{.}1.$

It is proposed to reduce the vibration displacement amplitude at the normal run speed of $500$ rpm to $80\%$ of its current value by inserting

a damping device.

The required damping ratio of the device is $.$

Your answer should be acurate to $\frac{+}{-}0\mathrm{.}01.$

If the mass of the machine is $600$ kg $,$ the damping coefficient of the damping device is

$kN\frac{s}{m}.$

Your answer should be acurate to $\frac{+}{-}1.$