3. The under-damped parallel rLC circuit C<a,a2-a2<0一 < →R=10.5> 2VC 85792) 2RC√LC By using complex numbers, the exponential response turns into a sinusoidal response U(t)=Ae+A2e”S12=-a±ya2-a ler:a2-a=y-1√a-a2=八a-a2(j=√-1) d natutal response frequency 1,2 c土/ d D(t)=Ae -toa+a,e (a-jad)t3. The under-damped parallel RLC circuit 8.57 ) 2 1 10.5 1 2 1 , 0 ( 2 0 2  0 −  − − −  → =  =  C L R RC LC     By using complex numbers, the exponential response turns into a sinusoidal response. d  s1,2 = −  j s t s t t A e A e 1 2 1 2 ( ) = + 2 0 2 s1,2 = −   − natutal response frequency d = − − − − 2 2  0  j t j t d d t A e A e ( ) 2 ( ) 1 ( )      − + − − = + : 1 ( 1) 2 2 0 2 2 0 2 0 2 let  − = −  − = j  − j = −