I am investigating the mathematics behind driven damped oscillators, I will then simulate it in matlab and observe the unpredictable long term behavior of the system. In order to create non-linearity in a oscillating spring I can no longer use hookes law but a form of it by introducing a power to the x term... for example F=-kx^3. Am I right? In order to find the force i will differentiate the potential energy equation with respect to position(x) because the F = Work done/ Distance moved. Or I will find the potential energy by integrating the force with respect to position. V(potential energy) = 1/4 - x^2/2 + x^4/4 dV/dx = F = x + x^3............. this is the double well potential no? How do I derive the formula for potential energy and/or the force. Now, because the force = x+x^3 and F=-kx^3 can I set these equal to each other and cancel some terms? So, x+x^3 = -kx^3..... no that would leave = x = -k.... F=-kx, the linear form of hookes law. Can someone point me in the right direction, either a good website outlining to mathematical concepts involved with this or can we have a discussion on the matter? I dont want to write too much right now. Thanks alot!