Strength (Σ₂/Σ₀, grey line) of the DM spiral arm at R = 8 kpc for the toy model. In this set-up, the potential amplitude is switched on and off every 1 Gyr. The long-dashed red line represents the shape of the potential (its height is arbitrary, for illustration purposes). Top: whole evolution. Bottom: detail of the strength of the potential around the three increasing steps of the potential (t = 1, 3, 5 Gyr). We observe that the potential takes ∼ 20 Myr to react to a change in the potential (impedance).