Q$.4$ A vibrating system is supported on four springs, It has a mass of $10$ kg $.$ The mass of reciprocating parts $2$ kg which move through a vertical stroke of $100$ mm with $5$ HM $.$ Neglecting damping. Find out the combined stiffness of the springs. So that the force transmitted to the foundation is $\backslash (1/20^\{\backslash$text $\{$th $\}\}\backslash )$ of the impressed force. The system crank shaft rotates at $1000$ r$.$p$.$m$.$ If under actual working conditions the damping reduces the amplitude of successive vibration by $\backslash (30\backslash \%\backslash ).$ Find:

$($i$)$ The force transmitted to the foundation at $1000$ r$.$p$.$m$.$

$($ii$)$ The force transmitted to the foundation at resonance and

$($iii$)$ The amplitude of vibration at resonance.