<p>This work investigates the influence of initial conditions on energy dissipation in linear systems undergoing parametric resonance. Specifically, we explore the semi-active control strategy of parametric anti-resonance, where stiffness modulation enables energy transfer between modes, thereby enhancing damping performance. Unlike traditional approaches, this study demonstrates analytically how the effectiveness of parametric excitation is not solely governed by system parameters, but is critically dependent on the initial conditions and their phase relation to the excitation. By applying the method of averaging, we derive closed-form expressions for the modal amplitudes and internal energy, allowing the formulation of two scalar quantities, the energy difference after one beating period and the integrated energy difference, which quantify the net effect of parametric excitation on dissipation. For the first time, both quantities are derived in general form including all system parameters and general initial conditions. Our results reveal that parametric excitation can either accelerate or retard dissipation depending on the initial modal energy distribution and phase shift. With both of the introduced quantities, a thorough description of the interaction of dissipation and parametric excitation becomes possible. This nuanced understanding challenges the conventional notion of parametric anti-resonance as universally stabilizing and has implications for the design of vibration mitigation strategies where initial perturbations are uncertain or variable.</p>