For an object not commonly used for a particular purpose, would mental designation to use in that way suffice if the designation was just for a one-off occasion? (bedeived)
For example, if a stick was used to prop open a window on a week when the mechanism to hold the window open broke if the stick was needed the following week for a different window who’s mechanism broke unexpectedly.
An item such as a stick or stone that isn’t used occasionally for this use needs to be prepared in one of two ways before shabbos in order to remove its muktza status. Either by permanently designating it for this use ( even by thinking), or if it is only going to be designated on a temporary basis, by making a physical change to the item, such as breaking it, or writing on it.
If this type of item would be used occasionally though then mental designation would suffice.
If it was used one week on a temporary basis, the fact that the next week the same thing happened would not change the halacha.
Shulchan Aruch O:CH 308-22, M:B 81-84, Tiltulei Shabbos pg. 80.