Wobbly windows were in fashion when I first started using Linux (indeed, they are part of why I started using Linux). But this feature has gone out of fashion and is not available on the GNOME desktop, which includes Ubuntu.
How to enable Wobbly Window GNOME Extension
Promising Wayland-based compilers can return this effect, but these effects, no matter how amazing they may be, are unlikely to be recognized in the higher GNOME shell (a project, as a rule, does not add or introduce support for parameters of other people’s default settings).
Therefore, the next best solution (for now) is to use third-party fixes and community extensions.
There are two different ways to enable shaky windows in the GNOME Shell in Ubuntu: one simple, the other involved.
Compiz alike Wobbly Windows Effect Extension
An easy way to enable the shaky window effect in GNOME Ubuntu 18.04 LTS (and higher) is to install the Compiz alike Wobbly Windows Effect extension from extensions.gnome.org (EGO):
Slide the switch off On to enable installation. The extension will be downloaded and enabled. After the wobbly window effect turns on, just grab any open window and rock it!
If you do not know how to install the extension in Gnome Shell, you can see this guide.
You can disable this extension at any time using the Extensions app on Ubuntu 20.04 LTS or GNOME Tweaks on Ubuntu 18.04 LTS.
Remember that this is a nice visual effect that will require additional resources for smooth operation.
You can also install the libanimation patch
The more accurate window wobble effect in the GNOME shell is also available as a GNOME extension, but it also requires the libanimation compiled patched version from the source code.
This method shows the actual compiz window wobble logic, broken and ported.
Complete steps on how to do this are listed on the corresponding GitHub page. The manual works for both Ubuntu 18.04 LTS and Ubuntu 20.04 LTS.
What extensions do you use in Gnome Shell?