Dynamic magnification factors of SDOF oscillators under harmonic loading

The magnification factor for the steady-state response of a SDOF system under harmonic loading is described in many structural dynamics textbooks; the well known analytical solution is easily obtained from the solution to the damped equation of motion for harmonic loading. The complete and steady state solutions can differ significantly. An analytical expression for the maximum response to the complete solution (steady state plus transient) remains elusive; however, a simple analytical expression is identified herein for the undamped case. Differences in the magnification factors obtained for both solutions are discussed.