- #1

- 2

- 0

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).

Considering a spring-mass system (like http://www.cs.toronto.edu/~faisal/teaching/notes/csc418/faisal/img/sm1.gif" [Broken]), 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?

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!

## Homework Statement

Considering a spring-mass system (like http://www.cs.toronto.edu/~faisal/teaching/notes/csc418/faisal/img/sm1.gif" [Broken]), 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?

## 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!

Last edited by a moderator: