The Date the activity happened field appears within a survey by default.
When creating a new survey it is listed on the right in the Your Survey Questions column
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If the Date Happened field has been removed from a survey, it will appear on the left in the Public Questions Library when on the Survey Editor page
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Click the Add button to add it to the Survey
Once the Date Happened field has been added to the survey, it can be used while creating/editing a story or submitting a survey response: Date Happened: change the date stamp of a story or survey response