If your Firefox browser window shakes or bounces, you can try the following actions to address the issue. Review the actions in the order listed below:

• Make sure you're running the latest version of Firefox. If you're not, try Upgrading Firefox.
• If your Bookmarks toolbar is displayed yet does not contain any bookmarks, you can add a bookmark to the Bookmarks Toolbar. Or, you can hide the Bookmarks Toolbar (Open the View menu, click on Toolbars, and uncheck Bookmarks Toolbar).
• If you have placed your Bookmarks toolbar items on another toolbar, such as the Navigation toolbar, and have hidden the Bookmarks toolbar, you can reset the Bookmarks toolbar. Remove the Bookmarks toolbar items. Drag the Bookmarks Toolbar items back to the Customize Toolbar window, and click Done. Replace the Bookmarks Toolbar items to where you want them.
• If you recently switched to a different Firefox theme, switch back to the default one.
  1. Open the Tools menu, and select Add-ons, to open the Add-ons window.
  2. In the Add-ons window, click the Themes icon.
  3. Select Firefox (default), and click Use Theme.
  4. Close Firefox, then start it again.
• If you are using a non-standard operating system theme or a program such as Windows Blinds, switch back to the default theme or disable the 3rd party application.
• If you have the extension eQuake Alert, one of its options shakes the screen when a new earthquake is reported. Disable this option.
• Try the standard diagnostic.

Based on information from Window shakes (mozillaZine KB)