conditional filling of data.frame - improve code

Dear useRs,

I would like to improve my ugly (though working) code, but I think I 
need a completely different approach and I just can't think out of my box!

I have some external information about which sample(s) belong to which 
experiment. I need to get that manually into R (either typing directly 
in a script or read a CSV file, but that makes no difference):
exp <- list(ex1 = c("sample1-1", "sample1-2"), ex2 = c("sample2-1", 
"sample2-2" , "sample2-3"))

Then I have my data, only with the sample IDs:
mydata <- data.frame(sample = c("sample2-2", "sample2-3", "sample1-1", 
"sample1-1", "sample1-1", "sample2-1"))

Now I want to add a column to mydata with the experiment ID. The best I 
could find is that:
for (i in names(exp)) mydata[mydata[["sample"]] %in% exp[[i]], 
"experiment"] <- i

In this example, the experiment ID could be extracted from the sample 
IDs, but this is not the case with my real data so it really is a matter 
of matching. Of course I also have other columns with my real data.

I'm pretty sure the last line (with the loop) can be improved in terms 
of readability (speed is not an issue here). I have close to no 
constraints on 'exp' (here I chose a list, but anything could do), the 
only thing that cannot change is the format of 'mydata'.

Thank you in advance!
Ivan