The apostrophe has three uses:
1) to form possessives of nounsApostrophes are NOT used for possessive pronouns or for noun plurals, including acronyms.
2) to show the omission of letters
3) to indicate certain plurals of lowercase letters.
Your case deals with the first (possessives of nouns:
Forming possessives of nouns
To see if you need to make a possessive, turn the phrase around and make it an "of the..." phrase. For example:
the boy's hat = the hat of the boy three days' journey = journey of three daysIf the noun after "of" is a building, an object, or a piece of furniture, then no apostrophe is needed!
room of the hotel = hotel room Once you've determined whether you need to make a possessive, follow these rules to create one.
door of the car = car door
leg of the table = table leg
• add 's to the singular form of the word (even if it ends in -s):
the owner's car James's hat
• add 's to the plural forms that do not end in -s:
the children's game the geese's honking
• add ' to the end of plural nouns that end in -s:
houses' roofs three friends' letters
• add 's to the end of compound words:
my brother-in-law's money
• add 's to the last noun to show joint possession of an object:
Todd and Anne's apartment
so in your case it should be Grandmother's experience