A vibration damping system for a transmission system, exhibiting a stiffness K, of a motor vehicle having a combustion engine, having a support member able to be rotationally driven around an axis X, having a moment of inertia I; and a pendulum flyweight mounted movably on the support member, the pendulum flyweight being tuned to a tuning order n, the pendulum flyweight having a first resonance order of an order lower than the tuning order n, and a second resonance order higher than the tuning order n; the moment of inertia I of the support being configured for any engine speed value within an engine speed range of the combustion engine from 600 to 5000/n revolutions per minute, and for a given stiffness K of the transmission system, the second resonance order of the pendulum flyweight is different from an order y*n, where y is an integer.