How to use a subdomain with a different URL but not duplicate content and effect SEO

I have a domain www.mydomain.com and want to create a new website that shares the same hostage account, so im planning on creating a folder www.mydomain.com/newsite.

I would like my new site to have its own domain name as its a different topic. so I might set up a domain www.newsite.com and direct it to www.mydomain.com/newsite.

This is all simple stuff, but im worried it will effect my seo because when I post information to the new website google will index too urls

'www.mydomain.com/newsite/first_post' and 'www.newsite.com/first_post'

This will result in duplicated content and effect my SEO rankings. Is there any way to fix this?

 

Any help please??

 

Will you redirect the traffic to it ?
If so this ain't good !

 

Yes basically id like two websites, two urls. both on the same servers but no duplicated content or adverse effects on seo

 

Any ideas how to solve this?