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I have a sine wave $w_0$ with a linearly increasing frequency $f_0$

$f_0(t) = r_0 \cdot (t - c_0)$

$w_0(t) = a \cdot sin(2 \pi \cdot f(t) \cdot t + \phi) $

I want to glue that sine wave to another sine wave at the moment $c_1$:

$f_1(t) = r_1 \cdot (t - c_1)$

$w_1(t) = a \cdot sin(2 \pi \cdot f(t) \cdot t + x) $ (NB $x$ instead of $\phi$)

at the point $c_1$ where $f_0(c_1) = f_1(c_1)$

But at that point the $w_0$ is in a certain phase. I need to plug that phase into $x$ (or at least in a way that the function stays continuous). How do I calculate the phase of $w_0(c_1)$?

Typhaon
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  • I don't think you can have $f_0(c_1) = f_1(c_1)$ since $f_1(c_1)=0$. – Jaap Scherphuis Mar 01 '23 at 17:03
  • I think is too complicatedly explained. You want to overlap two sine waves at a certain moment when they have their frequency match and you need the phase to match as well? Like paralleling two generators? In that case (in any case of paralleling AC) the coupling would be made at zero crossing with positive edge triggering. – WindSoul Mar 01 '23 at 17:10

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