Consider a close coiled helical spring of radius $R,$ subjected to a load $P .$ The spring consists of $n$ turns of wire with wire radius $r .$ The stiffness of the spring is

- 1
  
  $\frac{P R^{3}}{G I_{z}}$
- 2
  
  $\frac{G r^{4}}{4 n R^{3}}$
- 3
  
  $\frac{G I_{z} n r^{4}}{2 π R^{3}}$
- 4
  
  $\frac{P R^{4} 2 π n}{G I_{z}}$

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