"forced" and "obliged" have different meanings. Forced, means by the use of force or compulsion, such a using legal force, physical force, etc. The kidnapper forced the child into his car. The police forced their way into the building (through locked doors). The government/The court forced the parties to negotiate/ The court forced the parties to the negotiation table. Obliged means obligation. It is something you are expected to do. Society/friends have unwritten rules which you are expected (they expect you) to obey. A man is obliged to keep the door open for women, and he is obliged to help her into a seat at a restaurant. We are obliged to look after our elderly relatives, to care for the sick, to telephone or visit the sick/our friends/ our relatives. There are no written rules saying that we must do these things, but we are obliged to do them/ other people/society expects us to do these things. I can't force you to thank me for writing this answer, but you might feel obligated to do that. )))

I would say "forced" implies that someone is made to do something by physical force, threat, or consequence. "Obliged" means you have to do something even though nobody is actually making you do it.

If both words are used in a sentence referring to do something, obliged would be used when a person does something usually with good intentions. However, forced would be a person usually when a person does something but he/she didn't want to because he/she was told do something by someone. Hope this helps