Jquery, Remove class when width screen is 1050px

This is the JS code i'm using:

$("document").ready(function($){
var nav = $('#menu2');

$(window).scroll(function () {
    if ($(this).scrollTop() > 90) {
        nav.addClass("f-nav");
    } else {
        nav.removeClass("f-nav");
    }
});

But i can't seem to get this into my code.

function checkWidth(init){
/*If browser resized, check width again */
if ($(window).width() < 514) {
    $('html').addClass('mobile');
}
else {
    if (!init) {
        $('html').removeClass('mobile');
    }}}$(document).ready(function() {
checkWidth(true);

$(window).resize(function() {
    checkWidth(false);
});

And what i want is that when .f-nav is added to #menu2, when the screen is <1050 the classshould be removed.