An engine of mass \(200 \mathrm{~kg}\) is to be supported on four helical springs. When the engine speed is \(1000 \mathrm{rpm}\) there is a primary vertical periodic force of maximum value \(350 \mathrm{~N}\) due to the unbalanced reciprocating masses. Assume that the engine vibrates in the vertical direction with negligible damping, and there is no horizontal or angular movement.

(a) Find the stiffness of each spring to limit the maximum total periodic force on the foundation to \(25 \mathrm{~N}\).

(b) What will be the amplitude of vibration of the engine when its speed is \(500 \mathrm{rpm}\) ? Use the natural frequency found in part (a).