These examples show how the Nawderian theorem and the TriadicFrameworks stack apply to physical systems: wave resonance, energy quantization, acceleration drift, and dynamic coupling.
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Core TriadicFrameworks mathematical objects used:
A = Fโ ฯ_r T_f
If ฯ_r increases 10% and T_f decreases 5%, what is the net effect on A?
E = Dโ ฮฮ
If ฮ decreases 20%, how does E change?
a = T_fยฒ / Dโ
If T_f increases 10%, what is the percent change in a?
Net change: A increases by 4.5%.
Energy decreases 20%.
Acceleration increases 21%.
E = ยฝ Dโ ฯ_rยฒ + X
Describe how increasing ฯ_r affects the first term and total energy.
F = (T_f + Dโ) / โ(ฮฮ + ฯ_r)
Describe how increasing ฯ_r affects F.
R = X e^{-Dโ / ฯ_r}
Describe how increasing ฯ_r affects R.
p = Dโ ฯ_r - ฮฮ
Describe how increasing ฯ_r affects p.
ฯ(t) = โ(ฯโยฒ + T_fยฒ tยฒ / (Dโ + ฯ_r))
Describe how increasing ฯ_r affects spreading.
Fโ ร ฯ_r ร T_f โ A
ฮ + ฮ โ ฮฮ ร Dโ โ E
T_f โ T_fยฒ รท Dโ โ a