The support for a vibrating sorter consists of a plate sitting on a helical spring with a central plunger through the middle of the spring. The spring supports a mass of 850kg. the spring rate of this spring is 175N/mm. This arrangement provides the natural frequency required by the system. A design change has been suggested which would replace the single spring with four springs arranged around the plunger, with equal spacing. As the natural frequency is to remain the same, the new configuration will require the same overall spring rate. To fit into the restricted space, the new springs will have dimensions of D = 70mm, and d = 10mm.
Determine:
a) The no of coils required for each spring?
b) The maximum static stress in each spring in the modified design