(13)
Mῶ = X + Yi, M (ζ − g) = Z;
(14)
so that
Aῶ − Kῶi + gMaῶ + Maw = Maῶζ,
(15)
or
(A + Ma2)ῶ − Kῶi + gMaῶ + Maλ = Maῶζ.
(16)
Thus if the point of the gyrostat is made to take the periodic motion given by λ = R exp nti, ζ = 0, the forced vibration of the axis is given by ῶ = P exp nti, where