Hi,

I'm trying to solve for the modal transient dynamic response of a beam subjected to arbitrary loading in $\displaystyle t$ (time) and $\displaystyle x$ (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

$\displaystyle \ddot{T_{n}}(t) + T_{n}(t) = R(x,t) $

where $\displaystyle R(x,t) $ 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 $\displaystyle T_{n}(t) $? I'm not sure what to use as an initial solution guess.

Any help is much appreciated.

Thanks.