What would be the spring constant?

Question

3 identical springs have the same spring constant K. If these springs are joined to form a spring 3 times the length of an original spring what would be the spring constant of the new spring? Calculate to three decimal places.

Answer 1

k'=k/3

If there is only one spring:

You hang a mass m and the springs length increases by x so

W=k*x

k=w/x

All springs together

x'=3x (x for each spring) so

W=k'*x'=k'*3x

k'=w/3x

k'=k/3