What Are Physical Examples of Discontinuous Functions and Their Effects?

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can anyone tell me the physical examples of a discontinuous function?
and what is the effect of that discontinuous function on that particular physical prolem?
 
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Ahsan2011 said:
can anyone tell me the physical examples of a discontinuous function?
and what is the effect of that discontinuous function on that particular physical prolem?

What kinds of discontinuous functions can you think of? What kind of physical system can you think of that might follow a |sin(wt)| profile?
 
Think of a light switch...
 

Thread 'Prove that the integral is equal to ##\pi^2/8##'

Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...
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