The discussion revolves around the concept of damped harmonic oscillation, specifically focusing on the forces acting on a mass-spring system described by the equation F = -kx + bv. Participants are examining the implications of the damping coefficient, gamma (γ), and its sign in relation to the forces involved.
The discussion is ongoing, with multiple interpretations of the forces being explored. Some participants have provided clarifications regarding the direction of forces and the definitions of terms used in the equations. There is a lack of consensus on the correct formulation of the forces, indicating a productive exchange of ideas.
Participants are working under the assumption that the damping coefficient b is positive, and they are exploring the implications of this assumption on the equations governing the system. There is also mention of specific cases to consider based on the position of the mass relative to the equilibrium point.
I cannot see what that has to do with my post #44. The question I raised there was merely one of terminology: having resolved a vector into components in the ##\hat x## and ##\hat y## directions, as ##\vec v=x\hat x+y\hat y## say, what are the "components"? Are they ##x## and ##y## or ##x\hat x## and ##y\hat y##?Orodruin said:My point is that the x-component in one system is not the same as the x-component in another system. Taking the x-component of a vector in system A does not give you the same thing as taking the x-component in system B. In fact, they generally have both different magnitude and obviously correspond to different directions. As such, ”the x-component” is not coordinate invariant.
I mean, ultimately it comes down to if you want everyone to necessarily write vector arrows on everything that would need it in three dimensions also for one-dimensional problems. I don’t. I expect anyone that argues for this to also start writing double arrows on top of any variable representing string tension as it is actually a rank two tensor. What you actually call things later is not as important.haruspex said:I cannot see what that has to do with my post #44. The question I raised there was merely one of terminology: having resolved a vector into components in the ##\hat x## and ##\hat y## directions, as ##\vec v=x\hat x+y\hat y## say, what are the "components"? Are they ##x## and ##y## or ##x\hat x## and ##y\hat y##?
If anyone wants to continue this sidebar, I think we should do it by PM.
A good physicist ought to use proper symbols/notations/units everywhere, especially when writing a book, or when working on a project or when explaining things to others. If one is going to not use such symbols/notations/units for something, then justification and reminder for doing it like that, must be mentioned at appropriate places. If you are studying/doing some physics on your own for your own sake, then maybe not. This makes things precise & clear for everyone, otherwise it may lead to such disasters as mentioned in post#51.Orodruin said:I mean, ultimately it comes down to if you want everyone to necessarily write vector arrows on everything that would need it in three dimensions also for one-dimensional problems. I don’t. I expect anyone that argues for this to also start writing double arrows on top of any variable representing string tension as it is actually a rank two tensor. What you actually call things later is not as important.
You are missing the point completely. Writing out the projected equation is absolutely proper. There is not a single thing inappropriate about it. Do you also want to use double arrows on string tensions? If you want to be consistent with this point of view you must. I do not know any single source that does this, you are free to find counter examples if you can.NTesla said:A good physicist ought to use proper symbols/notations/units everywhere, especially when writing a book, or when working on a project or when explaining things to others. If one is going to not use such symbols/notations/units for something, then justification and reminder for doing it like that, must be mentioned at appropriate places. If you are studying/doing some physics on your own for your own sake, then maybe not. This makes things precise & clear for everyone, otherwise it may lead to such disasters as mentioned in post#51.
You are completely missing the point that I made regarding writing justifications and reminders if one is not going to do that.Orodruin said:You are missing the point completely. Writing out the projected equation is absolutely proper. There is not a single thing inappropriate about it. Do you also want to use double arrows on string tensions? If you want to be consistent with this point of view you must. I do not know any single source that does this, you are free to find counter examples if you can.