Okay, here we go:
It all comes down to finding the magnification factor for your model.
A quasi-static analysis simply ignores modal effects in the response of your model. I use it all the time.
What is the definition of "static"?
A static load is one where the rate of application (period of application) is long compared to the fundamental period of the structure. In terms of transmissibility, the ratio f_load/f_structure is going to be zero (or very near zero). This is equivalent to a transmissibility of 1. That is the structure will "see" all of the applied load. as f_load/f_structure approaches 1, the transmissibility will be greater than 1. This means the forces the structure sees will be equivalent to the applied load multiplied by the magnification (or sometimes called transmissibility) factor.
Now for any f_load/f_structure > 0 there will be some magnification of the load seen by the structure. However, for small values (typically less than 0.33) you won't introduce much error on your calculations by assuming your problem is static (transmissibility~1)
The advantage here is that you don't need to do a full transient analysis since modal effects are negligible. This saves computing time. Also if you can model your system as a 1DOF spirng-mass-damper you can easily calculate the magnification factor.
For a system to be modeled as 1DOF, the 2nd lowest mode must be AT LEAST one octave above the fundmental. Otherwise dynamic coupling can occur between modes and you will get very large responses.
For example, in the case of a half-sine pulse, if your system can be modeled as a 1DOF spring-mass-damper then all you need to know is the frequency ratio. The response spectrum for a half-sine pulse can be found in any dynamics book or from an internet search. if you know the frequency ratio R you can pick the Magnification ratio right off of the graph. Then you take the load and multipy it by the magnification ratio and apply it as a body force to your model. For a half-sine pulse, when the frequency of the structure is five times or more the frequency of the pulse, the magnification factor varies between 1 and 1.2. As a rule of thumb, when I do a shock analysis and the fundamental frequency of the structure is at least 5X that of the shock pulse, I simply apply the peak acceleration as a body load to my model.
My advice on how to solve the problem:
Run a modal analysis of your structure. The frequency of the shock pulse is 15.625 Hz. If the fundamental frequency is at least 78.125Hz then you can simply apply the 42G load to your model as a body force and run a static analysis.
If the natural frequency of your model is closer to the frequency of your shock pulse, you will need to come up with the magnification factor. The brute force method would be to do a full transient FEA. If your model isn't too large this is probably a good option. If the model is too large/complex to run then your only real choice is to try and convert it to an equivalent spring-mass-damper system. Then run a transient FEA on the simple model. Compare the peak response acceleration to the input acceleration. This will give you the magnification factor. Apply the factor to the 42 G's and run the static analysis on your full model.
As an aside, if the frequency of the structure is half or less than that of the shock pulse, your transmissibility will be less than 1. This is the isolation region.
