How to select specific form element in jQuery?

It isn't valid to have the same ID twice, that's why #name only finds the first one.

You can try:

$("#form2 input").val('Hello World!');

Or,

$("#form2 input[name=name]").val('Hello World!');

If you're stuck with an invalid page and want to select all #names, you can use the attribute selector on the id:

$("input[id=name]").val('Hello World!');

I prefer an id descendant selector of your #form2, like this:

$("#form2 #name").val("Hello World!");

http://api.jquery.com/descendant-selector/

although it is invalid html but you can use selector context to limit your selector in your case it would be like :

$("input[name='name']" , "#form2").val("Hello World! ");

http://api.jquery.com/jquery/#selector-context