Past modals and phrasal modals of obligation

EXPRESSING OBLIGATION OR NO OBLIGATION
We use must and have to to express obligation. The difference between them is : 

• We use must when the obligation is inside the speaker. it is a moral obligation
• We use have to when the obligation is outside the speaker. It comes from the situation.

• I must do some exercise to get fit.
• We have to be quiet in class. That´s the rule.

Note: Have to is not a modal verb.

We use don´t / doesn´t have to, needn´t and don´t /doesn´t need to to express no obligation.

• You don´t need to get up early. It is Sunday!
• she doesn´t need to wear a coat. It is warm outside.
• She needn´t cook tonight. We´re eating out. 

Firm obligation, etc. - must and have to 

The verb must only exists in the simple present and present perfect forms. 
While the present form can express obligation, necessity, certainty or strong probability, thepresent perfect forms only express a strongly felt opinion or supposition.

All persons	Present	Present perfect
Affirmative	must	must have
Negative	must not, mustn't	must not have, mustn't have

If other tenses are required, the speaker or writer must use forms of the synonymous modal verb "have to" .  This modal auxiliary has all normal tenses, including progressive or continuous forms; these are not common, but need to be used in some cases.

Principal tenses	Present	Present perfect	Past	Future
Affirmative:	has to, have to	has had to have had to	had to	will have to
Negative;	does not have to, do not have to , doesn't have to don't have to	has not had to have not had to	did not have to didn't have to *	will not have to won't have to

Exercise 1: Choose the best phrase to complete the sentences 
Exercise 2:  Modals of Obligation