$2.$ A reciprocating engine is installed on the first floor of a building, which can be modelled as a rigid rectangular plate resting on four elastic columns. The equivalent weight of the engine is $950$ kg $.$ At the rated speed of the engine, which is $600$ rpm $,$ produces a repeating force of $\backslash (30,000\backslash$mathrm$\{$~N$\}\backslash )$ when attached to a rigid foundation. The operators experience large vibration of the floor. It has been decided to reduce these vibrations.

a$)$ draw a free body diagram of the system. $[1$ point$]$

b$)$ Identify assumptions of the model problem. $[2$ points$]$

c$)$ Find a suitable vibration control method and its parameters to satisfy the following requirements:

$($i$)$ the force transmitted to the foundation should be less than $\backslash (10,000\backslash$mathrm$\{$~N$\}\backslash ).[7$ points$]$