Combinations solution of additive type to a two coupled weakly nonlinear second order differential equations which governed the motion of a two coupled nonlinear
oscillator subjected to linear parametric excitation and external excitation. We determined the modulation equations in the amplitude and the phase, steady state solutions,
the frequency-response equation and stability analysis of the steady state solutions by
MSMS. Numerical study of the frequency-response equations and stability equations
are given for different values of the parameters. Results are plotted in group of Figures.
Finally discussion and conclusion are given.