We consider the Hill equation with damping describing the parametric oscillations of a torsional pendulum
excited by varying the moment of inertia of the rotating body. Using the method of a small parameter,
we analytically calculate a fundamental system of solutions of this equation in the form of power series
in the excitation amplitude \epsilon with accuracy O(\epsilon^2) and verify conditions for its stability. In the first order
approximation in \epsilon, we prove that the resonance domain exists only if the excitation frequency \Omega
is sufficiently close to the double natural frequency of the pendulum; the corresponding equation of the
stability boundary is obtained
