scrolltop() is not work smoothly in chrome & safari but work in firefox

Starx

I am suggesting an alternative. The most favorable option to give to the smooth effect is to animate the change in position, to fake the easing.

Something like this

$(window).scroll(function(){
    $(".fixed").stop(false, true).animate({ "top" : $(window).scrollTop()}, 1000); 
});

Demo

This works great but when you starting scrolling with the scroll pane it starts stammering again.

But, to overcome this, you can use of debouncing techniques.

$(window).scroll(function(){
    $.doTimeout( 'scroll', 250, function(){
                         // ^ This time prevents the following code to run, 
                         //   if another scrolling occurs within this time

                         //   Thus enabling us to give a smooth scroll effect
                         //   Once the user is done scroll

        $(".fixed").stop(false, true) //break the queue fast
                   .animate({ "top" : $(window).scrollTop()}, 200);
    });
});

Demo