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I think you have pretty much answered your own questions. There are two ways to solve for the half sine acceleration pulse. Constrain the base and apply the acceleration as a body load (my preferred method, but the results are relative to the base) and the Base Excitation method in which the acceleration is applied as an actual displacement at the base. The 2nd method has the advantage of producing the absolute acceleration, but has the disadvantage of producing a non-zero velocity at the end of the half sine pulse (integral of the sine pulse acceleration) and a large amount of rigid body motion if the transient is continued for some time. In a real model it can also introduce issue of correct time-stepping. I don't think time-integration equation will significantly affect your results, but you can set it manually to a small number. It produces a sort of numerical damping equal to (time integration contant)/2pi. Damping is only significant when you have a steady state sinusoidal load at the resonant frequency. Â