This pendulum torsion damping device, intended to be linked to an internal combustion engine of main order N, comprises oscillating weights movably mounted on a support. The local order (OR) of the pendulum is sub-adapted, and substantially lower than N over a range of pendular displacement (DBT) close to the maximum displacement (C***). This device makes it possible to obtain effective pendular damping with a reduction in pendulum saturation phenomena at low engine speed, without causing saturation phenomena at high engine speed.
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