Swing

<script src="https://cdn.jsdelivr.net/npm/[email protected]/dist/bundles/anime.umd.min.js"></script>
<script>
  (function () {
    // Swing: the element swings from its top edge like a hanging sign that
    // has just been knocked, rocking back and forth and slowly coming to rest.
    // Usage: <div data-swing>…</div>
    // Optional: data-angle (degrees of the first swing, default 16),
    // data-duration (ms until it is still, default 2600), data-origin (the
    // pivot, as a CSS transform-origin, default "50% 0"), data-delay (ms before
    // the first swing), data-loop (swing again every so often while in view),
    // data-every (ms of rest between loops, default 1200), data-hover (also
    // swing on hover or tap).
    // Script use: animacious.swing(el) gives it a push from code.
    var DEFAULTS = { angle: 16, duration: 2600, origin: '50% 0', delay: 0, every: 1200 };

    function on(v) { return v !== undefined && v !== 'false'; }
    function reduced() { return window.matchMedia('(prefers-reduced-motion: reduce)').matches; }

    function play(el, done) {
      var s = el._swg;
      if (s.busy) { if (done) s.after = done; return; }
      if (reduced()) { if (done) done(); return; }
      s.busy = true;
      var d = el.dataset;
      function finish() {
        s.busy = false;
        var after = s.after;
        s.after = null;
        if (done) done();
        if (after) after();
      }
      var angle = d.angle === undefined ? DEFAULTS.angle : +d.angle;
      var swings = 3; // full back-and-forths before it settles
      var p = { t: 0 };
      el.style.transformOrigin = d.origin || DEFAULTS.origin;
      anime.animate(p, {
        t: 1,
        duration: +d.duration || DEFAULTS.duration,
        ease: 'linear',
        onUpdate: function () {
          // A damped pendulum: a sine wave that dies away.
          var a = angle * Math.exp(-2.6 * p.t) * Math.sin(p.t * swings * Math.PI * 2) * (1 - p.t * p.t * p.t);
          el.style.transform = 'rotate(' + a.toFixed(3) + 'deg)';
        },
        onComplete: function () {
          el.style.transform = '';
          finish();
        }
      });
    }

    function cycle(el) {
      var s = el._swg;
      play(el, function () {
        if (!on(el.dataset.loop)) return;
        clearTimeout(s.timer);
        s.timer = setTimeout(function () {
          if (s.visible) cycle(el);
          else s.waiting = true;
        }, +el.dataset.every || DEFAULTS.every);
      });
    }

    function init() {
      var io = new IntersectionObserver(function (entries) {
        entries.forEach(function (e) {
          var s = e.target._swg;
          s.visible = e.isIntersecting;
          if (!e.isIntersecting) return;
          if (!s.started) {
            s.started = true;
            setTimeout(function () { cycle(e.target); }, +e.target.dataset.delay || DEFAULTS.delay);
          } else if (s.waiting) {
            s.waiting = false;
            cycle(e.target);
          }
        });
      }, { threshold: 0.2 });
      document.querySelectorAll('[data-swing]').forEach(function (el) {
        if (el._swg) return;
        el._swg = {};
        if (on(el.dataset.hover)) {
          el.addEventListener('pointerenter', function () { play(el); });
          el.addEventListener('pointerdown', function () { play(el); });
        }
        if (!reduced()) io.observe(el);
      });
    }

    window.animacious = window.animacious || {};
    window.animacious.swing = function (el) { if (el._swg) play(el); };
    if (document.readyState === 'loading') document.addEventListener('DOMContentLoaded', init);
    else init();
  })();
</script>

<div class="sign" data-swing>Open</div>

<!-- or a gentler swing, repeating: -->
<div class="sign" data-swing data-angle="8" data-loop>Open</div>