wordpress and javascript plugin compatibility

I program a plugin where I use javascript, for example this line :

$( "input:radio[name=base]:checked" ).val();

When I put the shortcode on page and click the button to display an alert with the value obtained is not working but if I add the javascript script (cdn) if it works but the menu page generated Worpress stops working, I supposed that my plugin work with javascript that comes in the template. What is the problem?