What's in a name? (A and x)

There was one question after yesterday's class. I like to summarize my answer one more time here, since it touches upon the trivial but important and confusing concept. I may call the concept "all names are dummies."

For all names (A, x, y, z, v, omega, alpha, theta, ...) their meaning can change (sometimes very dramatically) depending on context.

The example here is the meaning of A and x in x = A cos (omega t + phi), in the context of "a person stretches a mass on a spring and then releases it to observe the consequent motion."

In this context, the initial stretch is A and the position of the mass at any arbitrary time thereafter is x.

However, the student noted that in previous lectures, x was used to mean the initial stretch (or compression) in many problems. Indeed this was the case. Actually, Hooke's law was introduced by using name x for the initial stretch or the initial compression.

The use of name x in apparently two different ways is not just me but also our textbook and other textbooks.

What you need to understand here is that in the SHM context we do need two symbols since we are considering the entire oscillation of a mass on a spring while in previous lectures we did not really need two symbols since we were not concerned with such a motion but we were just considering other things (like how much energy is stored in spring). So, in the context of the SHM, we have two things to describe -- the initial stretch and the time-dependent position of the mass -- which one should we call x? When given such a choice, x is usually used as a variable, namely in this case x is used to mean the latter.

Of course, it is extremely important to note that Hooke's law F = -kx holds at any time, in this problem, and so we are not comletely messing up with names, really.

I hope this is clear.