# Placing a zero at coordinate center when plotting with Ticks -> None

I'd like to plot a certain function where only its qualitative progession shall be emphasized. Thus, using the Ticks->None option seems to be appropriate. However, I need to place a zero at the axes origin. My first choice was to put it in the epilog.
As a toy example, consider the code

Manipulate[
Plot[(a + x)*Sin[a*x], {x, 0, 4*Pi}, Ticks -> None,
Epilog -> Text[0, {-.1, .5}]
],{a, 1, 5}
]


As you can see, the zero gets closer to the x-axis as a increases and in my real case, the zero is striked out by the x-axis for some parameter values.

How can I place a zero to indicate the axis origin, such that it is independent of the function drawn? Ideally, the x-axis is only drawn for non negative x and a zero would be placed right left to the point (0,0).

-
Do you need both axes? If you don't, you could use: Manipulate[ Plot[(a + x)*Sin[a*x], {x, 0, 4*Pi}, Ticks -> {{0}}, Axes -> {True, False},PlotRange -> {{0, Automatic}}], {a, 1, 5}]. The problem is "A tick label on the axes origin is not displayed" (alternatively, you could move the AxesOrigin) – Pinguin Dirk Jul 26 '13 at 9:27
Pinguin Dirk, nice idea! That actually solves another issue I'm having. Thanks. – Frederik Ziebell Jul 26 '13 at 10:17

I believe what you want can be had by using Offset coordinates:

Manipulate[
Plot[(a + x)*Sin[a*x], {x, 0, 4*Pi},
Ticks -> None,
Epilog -> Text[0, Offset[{-8, 8}, {0, 0}]],

A fast and dirty solution would be to freeze the Plotrange. For your example try: PlotRange -> {{-.5, 10}, {-15, 15}}.