How do you imagine a purely symbolic plot to look?

Not being able to grasp the concept of a purely symbolic plot, here is a Manipulate that explicitly substitute values:

x[a_, wo_, w_, t_] := a (wo Sin[w t] - w Sin[wo t])

Manipulate[

Plot[

x[a, wo, w, t], {t, 0, 100},

PlotRange -> {Automatic, {-2, 2}}

],

{{a, 1}, -1, 1},

{{wo, 1}, -1, 1},

{{w, .1}, -1, 1}]