Form Scheduler add-on for Google Forms can limit the number of responses and schedule to open or close the form based on the google calendar events.

Trial limitations: 
 - Accept during calendar events feature will cease functioning after 7 days

Free features:
 - Stop after Maximum responses
 - Stop at specific date
 
Features:
 - Schedule to collect form responses based on google calendar entries
 - Ability to schedule variable or fixed number of responses for every event occurances with overall maximum limit
 - Allow or stop accepting responses for recurrence events
 - Allow or stop accepting maximum responses for each recurrence events
   E.g. A lawyer or doctor can create appointment bookings by creating an accepting response event in the calendar and setting the daily limit to 20 or variable number of clients.
 - Stop reponses when maximum number of responses are reached
 - Stop responses after a specific date and time
 - Create schedules as once, hourly (90 minutes apart), daily, weekly, monthly, yearly with calendar recurrence
 - Custom closed message specification
 - Auto email creator after specified responses are collected 
 - Error reporting
 - The number of emails to be sent/day, trigger(s), it's run time etc. are restrained by your Quotas for Google Services. For details visit: https://developers.google.com/apps-script/guides/services/quotas

IMPORTANT: 
- Works best in Google Chrome
- Sometimes (rare circumstances) the scheduled calendar events may be activated with a lead/lag of +-60 minutes. Hence, this is not recommended for minute precision, complex workflows.