Transfer function with non zero initial conditions

[Wesker]

Hello guys, I'd just like to ask how can I formulate transfer function of second order differential system when I don't have zero initial conditions?
the equation is = y''(t) + B/m*y'(t) + k/m*y(t) = g y(0)= -L
don't care what parameters mean .. it's supposed to be solved in general

Thank you.

 

[S.G. Janssens]

Maybe it helps to introduce a new dependent variable $x(t) := y(t) - y_0 - v_0t$ where $y_0$ and $v_0$ are your initial position and velocity? Then rewrite the ODE in terms of $x$ with $x(0) = 0$ and $x'(0) = 0$.