If someone swore to fulfill a sick person’s request in order to calm him, what is the status of that oath?

A source-based Torah discussion of the question: If someone swore to fulfill a sick person’s request in order to calm him, what is the status of that oath? This localized discovery layer is limited to identifying the canonical issue for study and search. It does not provide individualized practical guidance or a new ruling; the Hebrew source remains controlling for the author’s reasoning, distinctions and conclusion.