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Guess I'll just burn (sh.itjust.works)

submitted 4 months ago by [email protected] to c/[email protected]

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[–] [email protected] 35 points 4 months ago (1 children)

As a physics major this is very true. The answers are always 0, 1, or π

[–] [email protected] 9 points 4 months ago (2 children)

No e?

[–] [email protected] 5 points 4 months ago* (last edited 4 months ago)

Usually it is e^t or something similar

[–] [email protected] 18 points 4 months ago (1 children)

Only if you are blowing shit up.

[–] [email protected] 4 points 4 months ago* (last edited 4 months ago)

If your signal looks like f(t) = K•u(t)e^at with u(t) = {1 if t≥0, 0 else}:

If Real(a) > 0, then your signal will eventually blow up.
If Real(a) < 0, then you signal will not blow up. In fact, your signal will have a maximum absolute value of |K|, and it will approach zero as time goes on.
If Real(a) = 0, it is either a complex sinusoid or a constant. In either case, it is bounded with maximum absolute value of |K|. It very much does not blow up.

So e pops up all the time in stable systems and bounded signals because the function e^at solves the common differential equation dx/dt = ax(t) with x(0)=1 regardless of the value of a, particularly regardless of whether or not the real part of a causes the solution to blow up.