Causality and the response function, the Kramer?s-Kronig relations are consistent with the principle that an effect not
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Causality and the response function, the Kramer?s-Kronig relations are consistent with the principle that an effect not precedes its cause. Consider a delta function force applied at time t = 0: whence Fw = 1/2?.?
(a) Show by direct integration or by use of the KK relations that the oscillator response function gives zero displacement, x(t) = 0, for t
(b) Evaluate x(t) for t > 0. Note that a(w) has poles at ? (w20?? ? p2)1/2 ? ?iP, both in the lower half-plane.
Transcribed Image Text:
F(t) = 8(t) = 2/1/² e -Ion dw a(w) = (w²w² - iwp)-1
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a The displacement under this force is xt 1b We want 1 1 0 27 J xt With og io the integral is faoee ...View the full answer
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