I wasn't sure where to post this problem, as it's physics related, but rather advanced in its math content (and it's a problem for my applied math course). 1. The problem statement, all variables and given/known data Considering a spring-mass system (like here), given that the nonlinear spring has force = qx^3, where q is the spring stiffness, what is the period of the oscillation when the mass is released from rest at x_0? 3. The attempt at a solution The equation of motion of the system is F=ma=-qx^3, so m*((d^2)x/dt^2)+q*x^3=0. Integrating, I get the energy of the system as (1/2)*m*((dx/dt)^2)+(1/4)*q*x^4. When released from rest at x_0, the system then has E=(1/4)*q*x_0^4. I haven't found examples of this type of problem anywhere, so any help would be greatly appreciated!