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He method of researching the dynamic properties of the railway crew in the action on it harmonic parametric perturbation, caused by the changing rigidity of the base of the rail, is set out. For such differential equations there are no regular methods of solving them, moreover, their exact solutions are not known at present, so they are used by approaching methods. A two-degree mechanical system with a harmonic parametric perturbation described by a system of ordinary homogeneous differential equations is considered. One of the hard-bone parameters is a function of time and varies from 2000 to 3000 N/m. To calculate the boundaries of dynamic instability (parametric resonance) a method of generalized Hill definers is used, which does not require the introduction of small parameters. The area of interaction of parametrically excited and forced vibrations has been determined.