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Network TheoryNetwork Functions

For a stable pair of complex poles -sigma plus or minus j omega_d, increasing sigma while keeping omega_d fixed causes the oscillatory transient to?

  • ADecay faster
  • BDecay slower
  • COscillate at zero frequency
  • DGrow without bound
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Correct Answer: A. Decay faster
Explanation: The envelope is e^(-sigma t); increasing positive sigma increases the decay rate while omega_d fixes the oscillation frequency.
Reference: Standard network theory: damping from pole location
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