Someone

@AdvilSell Yes. issues are going on right now. :/

Thanks dudee

If things goes well with visa then cornell

I would prefer higher studies gotta wait for complete covid update atm

😂

Graduated and ghar ka kaam

Hi

@Yuvraj hi

Yes

@HrishabhNayal no issues

@HrishabhNayal?

In that case, the result become obvious.

I think $a=0^{+}$ and $b=\infty$

@HrishabhNayal

And in the second integral put $t=-\frac{1}{X}$

$$\int_{a}^{b}f(t-\frac1t)\textrm{d}t + \int_{a}^{b}\frac{1}{t^2}f(t-\frac1t) \textrm{d}t =1$$

$\int_{a}^{b}f(t-\frac1t)\times \left(1+\frac{1}{t^2}\right)\textrm{d}t=1$

But anyway, the general scheme I used; is this.

Ahh I see, I had forgotten to change the limits here, yes yes my mistake.

Substitute $x=t-\frac1t$

$$\int_{-\infty}^{\infty}f(x)\textrm{d}x=1$$

Okay lemme write down

Put x = t - 1/t

It's simple just in the first integral f(x) dx

@HrishabhNayal are you sure about this. I think it's 1/2. Barring any calculation mistake.

@AjayMishra going to be graduated. Here xD

Need to finish things up

anyway, I will go now

It has happened many times

Yeaaa, that is actually very physical xD

As natural solution died

And resulted in a final 180 phase out

But in the other case, slow phasing out started to accumulate

In the one case Natural frequency always dominated and they kind of remained in sync

Yea, this seems a reasonable enough explanation. Maybe the point here was to actually considered what happened during the time of natural oscillations

Ahh okayyy

Okayy thats a constant Stretch

I am seriously wondering about the situation $w=0$ right now

Right?

So you said the speed has to be such that you can see at least one time period of motion

Okayyy This is definitely a very weird thing to think but I got your problem. But first I need to define a speed that is good enough here.

The train scenario will compare are systems at different instants

Do you want to view all of the systems at once or each system at some different instants?

Or wait no, not exactly the same

But you need the answer physically

?

You are essentially asking why the behavior of $x(w)$ as a function of $w$ for a fixed instant $t$ is so. Where the range of $w$ contains $w_0$

Okayyy I got the kind of problem you are asking for

Yeaa

Okayy