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).(adsbygoogle = window.adsbygoogle || []).push({});

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!

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# Period of nonlinear spring-mass system

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