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 the two solutions are discussed.