The force exerted by a reciprocating actuator is estimated as a weighted sum of three quantities: a reaction-mass acceleration, a baseplate acceleration, and a relative acceleration of the reaction-mass relative to the baseplate. In one embodiment, acceleration sensors measure the reaction-mass acceleration and the baseplate acceleration; and a displacement transducer measures a relative displacement of the reaction-mass relative to the baseplate. A double-differentiator generates the value of the relative acceleration from the second derivative of the relative displacement. In the sum, the relative acceleration is weighted by factor representative of the ratio of the difference between the masses of the reaction-mass and the baseplate to the sum of the masses of the reaction-mass and the baseplate.