JotForm is a free online form builder which helps you create online forms without writing a single line of code. No sign-up required.
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Jotform does not support automated sending of emails. Mails are only sent on form submission immediately. You could make a custom "Thank you" page where you could redirect user. In that php page you could save user to your database, and then send him emails periodically by cron on your webserver.
You can look at our guide for enabling POST data on custom "Thank you" pages.