React Hook recipe from https://usehooks.com. Demo: https://codesandbox.io/s/qxnmn1n45q

use-animation-example.js

import { useState, useEffect } from 'react';

// Usage
function App() {
  // Call hook multiple times to get animated values with different start delays
  const animation1 = useAnimation('elastic', 600, 0);
  const animation2 = useAnimation('elastic', 600, 150);
  const animation3 = useAnimation('elastic', 600, 300);

  return (
    <div style={{ display: 'flex', justifyContent: 'center' }}>
      <Ball
        innerStyle={{
          marginTop: animation1 * 200 - 100
        }}
      />

      <Ball
        innerStyle={{
          marginTop: animation2 * 200 - 100
        }}
      />

      <Ball
        innerStyle={{
          marginTop: animation3 * 200 - 100
        }}
      />
    </div>
  );
}

const Ball = ({ innerStyle }) => (
  <div
    style={{
      width: 100,
      height: 100,
      marginRight: '40px',
      borderRadius: '50px',
      backgroundColor: '#4dd5fa',
      ...innerStyle
    }}
  />
);

// Hook 
function useAnimation(
  easingName = 'linear',
  duration = 500,
  delay = 0
) {
  // The useAnimationTimer hook calls useState every animation frame ...
  // ... giving us elapsed time and causing a rerender as frequently ...
  // ... as possible for a smooth animation.
  const elapsed = useAnimationTimer(duration, delay);
  // Amount of specified duration elapsed on a scale from 0 - 1
  const n = Math.min(1, elapsed / duration);
  // Return altered value based on our specified easing function
  return easing[easingName](n);
}

// Some easing functions copied from:
// https://github.com/streamich/ts-easing/blob/master/src/index.ts
// Hardcode here or pull in a dependency
const easing = {
  linear: n => n,
  elastic: n =>
    n * (33 * n * n * n * n - 106 * n * n * n + 126 * n * n - 67 * n + 15),
  inExpo: n => Math.pow(2, 10 * (n - 1))
};

function useAnimationTimer(duration = 1000, delay = 0) {
  const [elapsed, setTime] = useState(0);

  useEffect(
    () => {
      let animationFrame, timerStop, start;

      // Function to be executed on each animation frame
      function onFrame() {
        setTime(Date.now() - start);
        loop();
      }

      // Call onFrame() on next animation frame
      function loop() {
        animationFrame = requestAnimationFrame(onFrame);
      }

      function onStart() {
        // Set a timeout to stop things when duration time elapses
        timerStop = setTimeout(() => {
          cancelAnimationFrame(animationFrame);
          setTime(Date.now() - start);
        }, duration);

        // Start the loop
        start = Date.now();
        loop();
      }

      // Start after specified delay (defaults to 0)
      const timerDelay = setTimeout(onStart, delay);

      // Clean things up
      return () => {
        clearTimeout(timerStop);
        clearTimeout(timerDelay);
        cancelAnimationFrame(animationFrame);
      };
    },
    [duration, delay] // Only re-run effect if duration or delay changes
  );

  return elapsed;
}

Should we use the argument passed to onFrame instead of Date.now() to calculate elapsed time?

Be sure to always use the first argument (or some other method for getting the current time) to calculate how much the animation will progress in a frame, otherwise the animation will run faster on high refresh rate screens. Check the example below for a way to do this.

Window.requestAnimationFrame() - MDN