How can I make a Java Swing animation smoother

I'm creating an animated slide transition in Java, and it is choppy on my current model MacBook Pro and on my year-old iMac, on Java 6, 7, and 8.

What can I do to make this animation appear smoother to the user on Mac OS X?

import javax.swing.*;
import java.awt.*;
import java.awt.event.ActionEvent;
import java.awt.event.ActionListener;

public class ScratchSpace {

    public static void main(String[] args) {
        AnimatedPanel panel = new AnimatedPanel();

        JFrame frame = new JFrame();
        frame.setContentPane(panel);
        frame.pack();
        frame.setLocationRelativeTo(null);
        frame.setVisible(true);

        panel.animate();
    }


    public static class AnimatedPanel extends JPanel {

        private float progress = 0.0f; // a number between 0.0 and 1.0

        public AnimatedPanel() {
            setPreferredSize(new Dimension(800, 600));
            setOpaque(true);
        }

        public void animate() {
            final int animationTime = 1000;
            int framesPerSecond = 30;
            int delay = 1000 / framesPerSecond;
            final long start = System.currentTimeMillis();
            final Timer timer = new Timer(delay, null);
            timer.addActionListener(new ActionListener() {
                @Override
                public void actionPerformed(ActionEvent e) {
                    final long now = System.currentTimeMillis();
                    final long elapsed = now - start;
                    progress = (float) elapsed / animationTime;
                    repaint();
                    if (elapsed >= animationTime) {
                        timer.stop();
                    }
                }
            });
            timer.start();
        }

        @Override
        protected void paintComponent(Graphics g) {
            Graphics2D g2d = (Graphics2D) g;
            int width = getWidth();
            int progressWidth = (int) (width * progress);
            g2