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This paper is concerned with the monotonicity of the period function for closed orbits of systems of the Liénard II type equation given by $${\ddot{x}} + f(x){\dot{x}}^{2} + g(x) = 0$$x¨+f(x)x˙2+g(x)=0. We generalize Chicone’s result regarding the monotonicity of the period function to planar Hamiltonian vector fields in the presence of a position dependent mass. Sufficient conditions are also given for the isochronicity of the potential in case of such a system.

Monotonicity of the Period Function of the Liénard Equation of Second Kind