The general question is : given an oscillating particle in a non-inertial reference frame:
- How would it appear from outside the non-inertial reference frame ?
- How would an observer inside that non-inertial reference frame see the movement of that particle?
- How different would the oscillation appear to the observer inside, in comparison to the same oscillation happening in an inertial reference frame?
This came up in the context of the following problem:
Suppose you have an incline plane (the angle is $\alpha$ ) and there's a crate with mass "M" that slides (with no friction) down the plane. On that crate there's a small pole with a tiny mass let's name it "m" tied to the pole with a weightless thread. I'm told that the mass "m" is not accelerating in respect to "M" and the question is: If I'm to give the mass m a small bump so that it's out of balance, what would be the frequency of the oscillations?
I'm not asking for a specific answer but more for conceptual guidelines.
Here is a schematic I drew: