Differentiating force to find potential energy

[Saxby]

A particle of mass m is moving along the x-axis and experiences a force F(x), also along the x-axis, given by F(x) = -kx. Deduce an expression for the potiential energy of the particle.



I tried intergrating both side (just to see if it gave me anything helpful). I got ∫F(x)dx=mv for the left hand side and -(1/2)kx^2 on the right hand side but i still don't have the answers. Any help would be much appreciated :)

 

[VantagePoint72]

The potential energy at some position $x$ of an object subjected to a conservative force (in one dimension) is $V = -\int_{x_0}^{x} F(x') dx'$. $x_0$ is arbitrary, since you can set the zero potential anywhere you like. You didn't need to integrate the left hand side explicitly.

Edit: Also, don't erase the homework help template. It's there for a reason, as this example demonstrates.

 

[Saxby]

Ok, I've found the answer and i understand how to do it. Thanks for your help :)