BLUF: I am trying to achieve sinusoidal motion that is acceleration driven so that it is analogous to a specific test. I would like to use the Dynamic, Implicit step so that later on I may account for nonlinearities. 

The question: Is there any way to force the dynamic, implicit step to obey zero initial conditions in both velocity and displacement (similar to the option in the Modal Dynamics step)?

The problem: When applying a base acceleration in a dynamic, implicit step, the output displacement function ends up with a constant*time term. Assuming initial velocity and displacement are 0, this term ends up as 1/omega where omega is the natural frequency of the part. This constant*time term is causing infinite growth in the displacement, which makes sense, but I would like to counteract this. Below is a list of attempts made so far in solving this and their outcomes:

1.  Apply a velocity of -1/omega: in theory, this should solve the problem because the integral of this term (and therefore the displacement function) is the negative of the constant*time term that results from the acceleration term assuming initial velocity and displacement are both zero. Because the acceleration and velocity terms are both applied as boundary conditions at the same locations, this results in an error that the nodes in those locations have conflicting boundary conditions. To remedy this, acceleration was instead applied as pressure since it should be analogous. This results in the pressure being overridden by the velocity boundary condition so there is no sinusoidal displacement. 
2. Damping: there was hope that applying a great enough damping would counteract the infinite growth, but it seemed to have no impact. Damping was applied as part of the material properties, and multiple values for alpha and beta were tested. It was also verified that each of these methods were impactful by applying them to the same model while a sinusoidal displacement boundary condition was used instead of the acceleration one; this resulted in the displacement amplitude tapering towards 0. 

There is also the option to apply a windowing function, such as a Hann function, to increase the amplitude in the beginning and decrease it at the end of the model, but this method only minimizes the effect of the constant*time term rather than eliminating it entirely.