In a mechanical system with a working member (22) performing a reciprocating periodic rotary motion and provided with at least one balancing subsystem (3, 4) comprising a balancing body (31, 41) coupled with the mechanical system working member (22) through the mediation of an elastic element, the negative effects of said mechanical system dynamic forces are reduced in such a manner that prior start of the mechanical system said balancing body (31, 41) is immobilized relative to a frame (1) and releases after the start of the mechanical system working member (22) if the required angular velocity ({omega}ip1) of stabilized operation of the mechanical system is achieved within the range of velocities admissible for balancing by the balancing body (31, 41) at the instant at which the mechanical system working member (22) is at a determined angular position ({delta}) relative to the mechanical system balancing body (31, 41). In an apparatus for making the above described method, a balancing body (31, 41) of a balancing subsystem (3, 4) is detachable connectable to a frame (1).
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