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Network TheorySecond-Order Circuits

In a critically damped second-order circuit, the natural response contains terms of the form?

  • A(A+Bt)e^(-alpha t)
  • BA sin(alpha t) only
  • CAe^(+alpha t) only
  • DA+Bt with no exponential
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Correct Answer: A. (A+Bt)e^(-alpha t)
Explanation: A repeated real characteristic root at -alpha produces the natural-response form (A+Bt)e^(-alpha t).
Reference: Standard network theory: critically damped response
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