I found this. https://www.youtube.com/watch?v=eSAmySbAafM It just plays Flipnotes, though.
As far as animation programs for PC go (excluding Adobe/Macromedia Flash and ToonBoom), I found these. Plastic Animation Paper http://animationpaper.com/ Pencil http://www.pencil2d.org/
I don't feel like there is much that fits the criteria of free without a lot of of limitations but as far as I know the best option might be the old version of Plastic Animation Paper (they are working on a new version).
Otherwise TVpaint is the best full featured in terms of hand drawn feel but its fairly costly. Also mentioned is Toonboom (Toonboom studio is the cheapest solution versus Animate or Harmony) but it also is costly and lacks the hand drawn feel since it is a vector based software.
Also worth a look is animating in a newer version of Photoshop (CS5+ I think) with the aid of plugins like AnimDessin2 which would facilitate the process and missing features. With Photoshop you get all the variety and option of brushes so there is no limit to what it can look like.
My favorite lite yet perfectly functional program is both great and it has it's older version free! It's called Plastic Animation Paper often called PAP. It deals in old school frame to frame drawing and a light box along with them futuristic capabilities of dem computers with copy paste and zoom and other nice functionalities. Check it out! Hope you like.it as much as I do! http://animationpaper.com/old-pap-free-download/
Opentoonz is pretty stable now. Can deffo get your bouncing ball on. Maybe a little complex but a lot of Youtube help out there.
The old PAP is free if you scroll down here: http://animationpaper.com/
If you have a 3DS, Flipnote is actually pretty simple and good.
PS has the clunkiest animation workflow! I'd suggest trying out a new program. Flash and Toon Boom have free trials. (Seriously, you can go through nine weeks of free Toon Boom Harmony, altogether.) There's also this for free, but it's pretty outdated/ not very intuitive: http://animationpaper.com/
The simplest program I've used has been Digicel Flipbook. The program is so simple, it barely gets in the way of animating, especially if you come from a background of animating on actual paper. It's used to do line tests in certain animation schools. However, since the software is so simple and bare bones, most people don't use it for doing much more than line tests.
Have you tried Synfig? It's free, and it seems to still be updated. I haven't used it in forever though.
TVPaint is a professional 2D animation suite that's meant for traditional animation, and has been used on a lot of traditional 2D animation films in Europe. It has slowly, but increasingly been seeing use here in US and Canada. The UI is very different from the Adobe layout we're all used to, so there's a bit of a steep learning curve to learning all the features and shortcuts.
The creator of Plastic Animation Paper is in the process of creating a new 2D traditional animation program that focuses on being as intuitive and as easy to use as possible. You might want to sign up for 1st access.