The authors study the Kuramoto model with inertia, a system of second order damped oscillators coupled through a sinusoidal function of phase differences. Each oscillator has an intrinsic frequency, randomly chosen from an even unimodal distribution. The connectivity is described by a convergent sequence of graphs whose limit is a graphon. The authors rigorously analyse the stability of the incoherent state (“mixing”) in the thermodynamic limit and show that it is stable for weak coupling and unstable for strong coupling. They identify the point of instability and show that it corresponds to a pitchfork bifurcation. Several numerical examples on Erdös-Rényi and small-world graphs are given, which verify the developed theory.