I get that if one fixed string tauts, that means the string has a tension, so the condition is T>0. (Correct me plz if its wrong)

But what if we have 2 strings (like in the image) and the question asks for the least value of w in order that strings are taut?

Whats the condition for two strings to taut..? Do both T1 and T2 have to be equal? What happens if one force is bigger than the other?