I need to convert Maxwell equation de/dt=(1/E)(ds/dt)+(s/n) into frequency domain equation. Here e=strain, E,n=constants, s=stress. If anyone has some idea, please let me know.
What't the problem? Use the Fourier transform
(1) (1/2π)∫-∞∞ de(t)/dt exp(iωt) dt = (1/2πE)∫-∞∞ ds(t)/dt exp(iωt) dt + (1/2πn) ∫-∞∞ s(t) exp(iωt) dt
I will denote by capital letters with tilda the Fourier transforms, i.e. E͂(ω), S͂(ω). Then, integrate by parts, e.g.
(2) de(t)/dt exp(iωt) = (d/dt)[e(t) exp(iωt)] - iωe(t) exp(iωt).
Let's suppose that E(t) ans S(t) vanish at ±∞. You get
(3) -iωE͂(ω) = -(iω/E)S͂(ω) + S͂(ω)/n
In all, your equation becomes
(4) E͂(ω) = [(1/E) + (i/(nω))]S͂(ω)
Dear Ajay Goyal,
Please take into account that I assumed that both functions e(t) and s(t) vanish for t→-∞, and for t→+∞. You have to check if my assumptions are correct.
If the functions are defined only on a limited interval of time, [t1, t2], and at the ends of this interval these functions vanish, then my calculus is still O.K. But if the functions, or one of them, don't vanish at one of the ends of the interval, then you need for that function the Fourier series, not the Fourier integral.
Please check and tell me.
- Badges
- Science topic
- Similar topics
- Theoretical Physics
- Time