Is a timed redirection from one WP page to another possible?

I want to make some pages on my site only available to registered users belonging to a community. They all have a password to access a protected page. I would like the sidebar for these users to be different.
But if I cange the sidebar on the password protected page, all users can access the options. If, on the contrary, I leave the standard sidebar, the community users don’t know they have different options available without going further.
One possibility would be for this page to propose a “Proceed” link but the user would of course have to click it. Boring for frequent users!
Is there a script or PHP snippet I could use within the textarea (editable in WP write page) whioch would allow the page to automatically forward to another after a few seconds once the password has been accepted?
All the scripts I have seen need to modify the headers which doesn’t seem to be a solution.
I’d be grateful for any ideas.