That's just the standard which in your case is and that has the general solution:
assuming is integrable in the interval . That solution is via variation of parameter
I'm trying to solve for the modal transient dynamic response of a beam subjected to arbitrary loading in (time) and (measurement along the length of the beam). I've already solved for the eignefunctions that describe the beams displacement. I'm now trying to solve for the temporal solution. I get to
where is an arbitrary function determined from some integration and operation on the forcing fuction.
Question: Does anyone know how to obtain a solution to this equation for ? I'm not sure what to use as an initial solution guess.
Any help is much appreciated.