Is "get" (in the sense of "become/make") appropriate for formal writing?
Solution 1:
This may depend on the particular research community. I can say, at least in spoken presentations in a workshop or conference, many communities may find using 'get' just fine... but many other communities would not.
I would personally like to avoid 'get' in formal writing, I guess you mean research articles. To be sure, you should try to check if the community you belong to uses it in their literature. But, if its for emails or blogs, it maybe alright.
Solution 2:
Get is fine to use if it fits, but it is probably too general for most cases where you might use it in a scientific paper. Consider precise substitutions:
got a reaction => produced a reaction
test subjects got rashes => test subjects exhibited rashes
we got results using a .04% solution => results were achieved using a .04% solution
That kind of thing. You can use get where appropriate, though:
In many cases, test subjects got up from their chairs and left the room rather than answer any more questions.
And one place you may definitely use it is in emails to your colleagues:
Good news! We got our funding! Booyah!
Solution 3:
Get has a lot of uses in English. It's the Causative/Inchoative form of both be and have. That is, it can represent either come to be (= become) or come to have when it's inchoative -- Inchoatives are intransitive and refer to change of state -- or it can represent either cause to be or cause to have when it's causative -- Causatives are transitive and refer to causing change.
- Stative: He was tired/sick/here/mad/arrested/writing.
- Inchoative He got tired/sick/here/mad/arrested/writing.
- Causative He got me tired/sick/here/mad/arrested/writing.
Consequently, get can be used in most constructions and idioms that involve either be or have. And there are an awful lot of them.
As far as its usage in scientific papers is concerned, I agree with Karthik that this depends entirely on the traditions of the research community. Nobody should attempt to write (let alone publish) scientific research in any field without having read many, many papers in the same field, and by that time, they should be aware of the traditional writing styles and conventions in their field.
Oh, and most of the examples provided in the OQ are not participles, by the way.