Plotting a 3D piecewise function?

I'm trying to plot a 3d graph, here's what I want to do: I have a function f that is dependent on time t and on another variable u, and is also piecewise; i.e. f(t,u) = g(t) if u > 0 and f(t,u) = h(t) if u < 0.

I'm wondering what would be the best way to plot a graph of f(t,u) for all values of t between 0 and 100 and all values of u between -50 and 50?

(I might also mention that both g(t) and h(t) have the imaginary number in them if that would affect anything)

Thanks to anyone who can help :)