Engineering Board Exam Reviewer · Applications: Electric Circuits and Vibrations · hard

A damped system obeys x''+4x'+13x=0 with x(0)=1 and x'(0)=0. Find x(1).

  1. -0.134
  2. -0.121
  3. -0.147
  4. -0.096

Answer

B. -0.121

Solution

r= -4 (16-52)2=-2 3i, so x=e-2t(A 3t+B 3t). x(0)=1 A=1. x'(0)=-2A+3B=0 B= 23. Then x(1)=e-2≤ft( 3+ 23 3 ) -0.121.

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