In this paper, we present an investigation of the dynamics of electrically actuated carbon nanotubes (CNTs) resonators including the effect of their initial curvature due to fabrication (slack). A nonlinear arch model is used to simulate the motion of the slacked CNT. A reduced-order model using a multimode Galerkin procedure based on the mode shapes of the straight un-actuated CNTs is derived. The reduced-order model equations are integrated numerically with time to reveal the steady-state response of the CNT when actuated by a DC load superimposed to an AC harmonic load. A perturbation method, the method of multiple scales, is used to obtain analytically the forced vibration response due to DC and small AC loads for various slacked CNT. Results of the perturbation method are verified with those obtained by numerically integrating the reduced-order model equations. The effective nonlinearity of the CNT is calculated as function of the slack and the DC load while using a beam model for the CNTs showing a softening dominant behavior.