Hi!
Let's make a brief comment about the superposition principle, adding
to the excellent observations of Jack U.
1. The principle itself. It states that, within the context of a
certain system, we compare the "effect" of different "causes". If
causes C1 and C2, acting separately, have effects E1 and E2 respectively,
then the cause C1+C2 has the effect E1+E2.
2. When does it apply formally? Whenever the relation between C and E
is "linear", i.e. E = f(C) = K*C. Here K can be a "linear operator", for
example an integral or a diff. equ. operator.
3. When does it apply in nature? We can suspect that the answer is
"almost never", it is just an approximation. This approximation may be
very good or not, only direct observation and experimentation can decide.
4. Main remark: if it is a good approximation depends crucially on
how the values of C and E are defined, i.e. on the way we describe mathe-
matically the process. For example: if a car makes 70 decibell of noise and
a truck makes 80 db noise, the two together certainly do not make 150 db.
Indeed, the db is a measure of noise by the log of the energy and there
is no reason why these logarithms should add.
5. Examples. Particularly for an intro course, the simplest are the
best. Hooke's law of streching of a spring (or a wire, etc.) are very
appropriate. By the way, this also leads to the need of using vectors
to describe forces, so that we can "add" them.
Regards. Emilio.