I am looking for further examples for two functions $f,g$ such that $f \neq O(g) \land f \neq \Omega(g)$. I have found the old thread Is there a function thats not in Big O and not in Big Omega? where this also discussed, however I wanted to know whether there are also more "basic" functions which fulfill this as opposed to functions with multiple exponentials and piecewise defined functions?
For example if I set $f=sin (x)$ and $g=x\cdot sin(x)²$ would this fulfill the above mentioned property?