(3)
where Qr now stands for a component of extraneous force. In a free oscillation we have Q1, Q2, ... Qn = 0, and if we assume
qr = Ar eiσt,
(4)
we obtain n equations of the type
(c1r − σ2a1r) A1 + (c2r − σ2a2r) A2 + ... + (cnr − σ2anr) An = 0.
(5)
Eliminating the n − 1 ratios A1 : A2 : ... : An we obtain the determinantal equation
Δ (σ2) = 0,