We hang a square circuit of side a, of resistance R and of mass m by a spring of stiffness k. We choose z=0 at equilibrium, where z is the coordinate which corresponds to the middle of the frame. We apply a magnetic field perpendicular to the frame such that B=0 for z>0 and B=B₀ for z0 exp(-?t) with complex ?. Show that there exists a critical value R₀ of R below which ? can be chosen as real. Qualitatively describe the movement of the circuit in the two cases R>R₀ and R0. 5) What is the energy dissipated by the Joule effect in the circuit at each instant as a function of z? Give without calculation the total energy dissipated by the Joule effect between t=0 and t=+?.