I suspect there may be periodic solutions. For $A = 1$, numerically plotting the solution with initial conditions $x(0)=0, \dot{x}(0) = 0.442091320614410, \ddot{x}(0) = 0.774949154843236$$$x(0)=0, \dot{x}(0) = 0.442091320614410, \ddot{x}(0) = 0.774949154843236$$ I get this:
This looks to me like an approximation of an unstable periodic orbit.
I suspect there may be periodic solutions. For $A = 1$, numerically plotting the solution with initial conditions $x(0)=0, \dot{x}(0) = 0.442091320614410, \ddot{x}(0) = 0.774949154843236$ I get this:
This looks to me like an approximation of an unstable periodic orbit.
I suspect there may be periodic solutions. For $A = 1$, numerically plotting the solution with initial conditions $$x(0)=0, \dot{x}(0) = 0.442091320614410, \ddot{x}(0) = 0.774949154843236$$ I get this:
This looks to me like an approximation of an unstable periodic orbit.
I suspect there may be periodic solutions. For $A = 1$, numerically plotting the solution with initial conditions $x(0)=0, \dot{x}(0) = 0.442091320614410, \ddot{x}(0) = 0.774949154843236$ I get this:
This looks to me like an approximation of an unstable periodic orbit.
