Problem-
1) A coil spring with the radius of R is subjected to a load P. The radius of this spring is r and rolled n times.
1) Define the torsion moment Mt (which is constant through the length and the function of P and R) and derive a formula of the spring deflection of δ by Mt with the function of δ = δ(P, R, G, r, n) using Energy method.
In the above Free-Body Diagram, the deflection by P is ignored. It is assumed that the, torsional moment is only the energy. Then, 
and L is the total length of spring under torsion (2ΠRn = Rθ* and dz = Rdθ. By using this relationship, it is convenient to change the integral from 
2) Calculate spring coefficient k = P/δ and discuss the design on how much spring radius r should be changed to increase k two times
3) We consider a coil spring that P is applied at the end (instead of the centre). Calculate the deflection from torsional moment Mt and bending moment Mb and, then discuss the deflection from the torsional moment Mt compared to the result of 2-1)