gear used on cassete deck door to open slowly?

Don’t know if there is a technical description other than ‘soft open’ mechanism - as opposed to ‘soft close’ mechanisms for applications such as cabinet drawers.
For small applications struts/dampers may be less practical.
Springs are more typically (lower cost) and can be designed/spec’d to application - door weight and speed required.

Here is another patent example that may help illustrate spring mechanism:

You can also find examples in auto interiors. Small compartment doors and cup holder mechanisms come to mind.