Turbochargers are key components of engine air-paths that must be carefully considered during the development process. The combination of fluid, mechanical, and thermal phenomenon make the turbocharger a highly dynamic and nonlinear modeling challenge. The aim of this study is to quantify the dynamic response of the turbocharger system across a frequency spectrum from 0.003 Hz to 500 Hz, i.e., for exhaust gas pulsation in steady state, load steps, and cold start drive cycles, to validate the assumption of quasi-steady assumptions for particular modeling problems. A waste-gated turbine was modeled using the dual orifice approach, a lumped capacitance heat transfer model, and novel, physics-based pneumatic actuator mechanism model. Each submodel has been validated individually against the experimental measurements. The turbine inlet pressure and temperature and the waste-gate actuator pressure were perturbed across the full frequency range both individually and simultaneously in separate numerical investigations. The dynamic responses of turbine housing temperature, turbocharger rotor speed, waste-gate opening, mass flow, and gas temperatures/pressures were all investigated. The mass flow parameter exhibits significant dynamic behavior above 100 Hz, illustrating that the quasi-steady assumption is invalid in this frequency range. The waste-gate actuator system showed quasi-steady behavior below 10 Hz, while the mechanical inertia of the turbine attenuated fluctuations in shaft speed for frequencies between 0.1 and 10 Hz. The thermal inertia of the turbocharger housing meant that housing temperature variations were supressed at frequencies above 0.01 Hz. The results have been used to illustrate the importance of model parameters for three transient simulation scenarios (cold start, load step, and pulsating exhaust flow).