Flipping a spring makes no difference. Spring compression is irrespective of spring orientation.
In general, you get varying spring rates by varying the spring [geometry.](https://www.hypercoils.com/wp-content/uploads/hyperco_dual-rate-spring-400×400.jpg) You can do it by changing the pitch of the spring like in that image, or you can change the coiled diameter, or the wire diameter or cross sectional shape. There are lots of different kinds of springs and you can do all sorts of weird things to their shape to get a varying force throughout their range of travel.
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