The Mishna on Bava Kamma 37a gives various examples of how an ox can be mu'ad in one scenario, while Tam in another. Some examples mentioned in the mishna include: an ox which is predisposed to goring other oxen while being a tam for other animals; or an ox which is mu'ad to gore calves but will not pick on oxen of its own size. The mishna then relates that R' Yehuda was asked about whether an ox could be mu'ad for shabbos but not during the week. He responded that the owner would pay nezek shalem if the ox gored on shabbos, but would only pay half during the week.
Rashi and Tosafos have different explanations as to how this ox came to be mu'ad on shabbos. Rashi explains that the ox was essentially bored - since it worked all week but had nothing to do on shabbos, it gored. Tosafos explains (quoting the Yerushalmi) that it saw people wearing different clothing and did not recognize them and gored them because the ox thought they were strangers.
I heard an interesting vort on the concept of mu'ad l'shabbos from R' David F. He said that a woman once came to the Rogechover (sp?) and complained that her child would not nurse on shabbos. He responded "you have a baby who is mu'ad l'shabbos." He explained to her that the baby was not used to seeing her in shabbos clothes and did not recognize her. He suggested that the mother change into her regular (weekday) clothes when she nursed the baby. This solved the problem.
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