On the response of antisymmetric constant force oscillators: Exact and approximate solutions

•Antisymmetric constant restoring force oscillators are considered.•Exact solutions for the response of conservative systems are presented.•Square wave and triangular wave functions are used for this purpose.•Approximations are also obtained for the response of damped oscillators.•Averaging in terms of square wave and triangular wave functions is utilized for this purpose.

Oscillators with an antisymmetric constant restoring force are considered in this paper. Their general characteristics—the corresponding amplitude and period of motion, are discussed first. Then, the exact solutions for acceleration, velocity and motion of such conservative oscillators are presented. One of them includes the use of the square wave and triangular wave function, which are utilized to develop a procedure for finding approximations for the response of damped antisymmetric constant force oscillators. Comparisons with numerical solutions are provided to demonstrate their accuracy.