The time varying root locus (TVRL) method has been used for investigating the transient analysis of a quadrature oscillator circuit with undesired operating points. The TVRL trajectory of the dominant pole corresponding to the time varying periodic solutions obtained by SpectreRF has been analyzed to predict the sinusoidal and relaxation oscillation mechanism. The numerical QZ algorithm has been practiced to compute the characteristic roots relative to periodic steady-state (PSS). The proposed circuit is analyzed with TVRL to check if it avoids the relaxation process and confirms the proper sinusoidal operation of oscillator or not.