Finding the potential of a force

Question

Hi

 

I have been asked to find the potential V(x) of the force F(x)=k(x-L).

 

Can anyone help me with this please? Thanks

Answer 1

Whenever you have a potential V(x) as a function of x, the force F(x) is 

 

F(x) = -dV(x)/dx

 

Then

 

V(x) = -∫F(x)dx = -∫k(x - L)dx = -k(x - L)²/2 + c,

 

where c is a constant.  To find c, you would need to state a known value of V₀ at some reference point x₀.