Considering the nonlinear system x_ = and y_ = z z_ = 􀀀az 􀀀 by 􀀀 f(x) (2) which it has an oscillatory behavior is demonstrated in the case that f(􀀀x) = 􀀀f(x), that by replacing the f(x) function f(x + B sin !t), and will -lores of B and ! large enough the system is oscillatory motion large amplitude. In fact all solutions tend to Origin neighborhood so small as you like. To make this demonstration we proceed as follows: Initially disturbed function in terms of x is expressed and B sin(!t), to proceed to calculate the average function. Then test for h(; x) = f(x + B sin ) 􀀀 f0(x;B), There is a continuous function H(; x; 1! ) such that jH(; x; 1 ! )j !(!) where (!) ! 0 when ! ! 1 and performing substitution z = s + 1 !H(t; x; 1 ! ) shows that the perturbed system is equivalent to the following system x_ = and y_ = z +1! H(t; x; 1!) z_ = 􀀀az 􀀀 by 􀀀 F0(x;B) 􀀀 a 􀀀 1! H(t; x; !) 􀀀 1! @H @x and Thus it is proved that for ! large enough, the averaging system is a good approximation of the system disturbed. This is that any solution of the perturbed system is sufficiently close to a solution of averaging system. There is also evidence that B0 such that B > B0, the solution trivial averaging system is asymptotically stable values of ! sufficiently large. Finally it is proved that for B and ! enough large system has disturbed oscillatory motion large amplitude, that is, the disturbance has destroyed the large amplitude oscillations.