Calculate the spring constant for a linear spring given the spring potential energy and the extension displacement.

Example question:

A linear spring has a potential energy of 7.3 J when it is stretched 0.29 m. What is the constant for this spring?


spring potential energy: Us = 7.3 J

displacement: x = 0.29 m

Starting formula

Algebra: multiply each side by 2

Algebra: 2's cancel on right

Algebra: divide each side by x^2

Algebra: x^2's cancel on right

Algebra: switch left and right

Plug in numbers with units

Multiply: (2)(7.3)/0.29^2 = 173.602....

Final result with significant figures and unit