On a physics test today, one of the free response questions asked about a non linear spring where F=-kx^3. Now I got everything right, but there was one thing that I felt I did not have any concrete mathematical basis for--I just thought about it. I had to say whether increasing the amplitude would increase, decrease, or keep the period the same. I said decrease (which, apparentely is correct) just by considering the exponential-esque relationship between displacement and acceleration and by comparing that to the constant period SHM. Can anyone explain the mathematics better than this? Thanks (sorry--unnecesarily long post).