Q$-5(15)$

A reciprocating engine, running at $600$ rpm $,$ mounted on an elastic foundation is found to have excessive vibrations. The engine has a mass of $900$ kg and produces a disturbing force of magnitude $1500$ N at the rated speed. It is required to eliminate the vibration of the engine by the use of a spring$-$mass dynamic vibration absorber$.$ Determine:

a$.$ The mass to be added if the spring is chosen has $\backslash (\backslash$mathrm$\{$k$\}=50\backslash$mathrm$\{$kN$\}/\backslash$mathrm$\{$m$\}\backslash )$

b$.$ The amplitude of vibration of the added mass.

Ignore any damping