A cart of mass \( m \) is placed on a level, horizontal track. The cart is attached to a specialized magnetic spring setup that exerts a non-linear restoring force on the cart. The force exerted on the cart by the setup is given by the equation \( F_s = -\beta x^3 \), where \( \beta \) is a positive constant and \( x \) is the displacement of the cart from its equilibrium position at \( x = 0 \). Frictional forces between the cart and the track are considered to be negligible. The cart is displaced to an initial position \( x = A \) and released from rest.