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

An undamped system obeys x''+4x=8 2t with x(0)=0 and x'(0)=0. Find x≤ft( π4 ).

  1. 0.785
  2. 3.142
  3. 1.571
  4. 2

Answer

C. 1.571

Solution

The forcing frequency equals the natural frequency (resonance), so try xp=At 2t: xp''+4xp=4A 2t=8 2t A=2. With x(0)=x'(0)=0 the constants vanish, so x=2t 2t and x≤ft( π4 )=2· π4·1= π2 1.571.

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