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Width of plots


When making several plots, e.g. using

f[x_] = Sin[x];
g[x_] = 1000*Sin[x];

p1 = Plot[f[x], {x, 0, 2Pi}, ImageSize -> 400];
p2 = Plot[g[x], {x, 0, 2Pi}, ImageSize -> 400];

the absolute position of the y-axes won't coincide despite the total 
image size being the same. This seems to be caused by the different 
width of the tick labels.

Is there a possibility to rescale the images in such a way that the 
y-axes positions coincide in two different plots and the x-axes scale 
stays the same?

Thanks for your help,
Michael


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