For the post "Rectified Waveform To The Rescue",
The response using a full normal wave is just the superposition of a rectified wave and an inverted rectified wave, but frequency halved. The results does not contradict.
But the expression,
\(\cfrac{d^2T}{d\,t^2}=i\omega_dV_oI_oe^{i2\omega_d t}cos(\theta)\)
is a complex valued frequency \(i\omega_d\), as needed in the post "Complex Frequency And SuperConductivity". Which is dealt with,
\(\cfrac{d^2T}{d\,t^2}=e^{i\pi/2}\omega_dV_oI_oe^{i2\omega_d t}cos(\theta)\)
\(\cfrac{d^2T}{d\,t^2}=\omega_dV_oI_oe^{i(2\omega_d t+\pi/2)}cos(\theta)\)
A phase delay in time.
That is to say, a complex number, \(e^{iA}\) multiplied to a time function \(e^{iwt}\), travels back or forth in time by a phase \(A\).
