$3.$ Design a helical spring using the following data. The spring is to be acted upon by a load varying between $300$ N and $900$ N $,$ as shown in the figure. The spring deflection needs be around $15$ mm and outside diameter of the spring needs be within $48-50$ mm$.$

Validate your design by giving

please solve step by step to undustand

$(1)$ The wire diameter, d

$(2)$ The surge frequency, f

$(3)$ The corresponding fatigue design factor of safety and also answer

$(4)$ Whether the spring will buckle in service

$(5)$ Whether the spring will yield under shearing