Applying a force incrementally

I am attenpting to run a simulation under specific requirments i was given. 

The simulation is a pressure vessel with legs welded onto it. That legs gets bolted to a containment frame, which then in turn gets bolted to a vessels floor.

I ran the simulation with the force of the liquid at a 30 degree static heel.  I now have to add the following forces:

"Acceleration of +/-.5g parallel to the deckhouse" (simulating a vessel moving forward and backward)

"Acceleration of +/-1g perpendicular to deckhouse" (stimulating a vessel moving up and down)

My question is, is there a way to apply this force incrementally? Meaning the force starts at -1g and moves to +1g over a period of lets say 5 seconds. 

My initial thought would be to multiply the mass (x1 for 1g and x.5 for .5g) and apply that force,but i need to show a time span of how these forces effect the pressure vessel moving. i cannot seem to figure out how to apply these force as described.

Thank you for your time!