Duty: noun meaning : something you must do or you have to do because it is morally or legally right [= obligation]
So use of word “obligatory” is not necessary with "duty"..
Apart from the meaning related to work/service the word “duty” has also other uses such as:
- Do your duty
- It is somebody's duty to clean the floor.
customs duty (=tax paid on goods coming into the country)
stamp duty, double duty (a thing capable of serving two purposes) , heavy-duty
Obligatory: adjective meaning: something required as a matter of obligation; mandatory or compulsory.
- For me toreply to your post is desirable but not obligatory.
- Mathematics is an obligatory subject in the course