(*^ ::[ Information = "This is a Mathematica Notebook file. It contains ASCII text, and can be transferred by email, ftp, or other text-file transfer utility. It should be read or edited using a copy of Mathematica or MathReader. If you received this as email, use your mail application or copy/paste to save everything from the line containing (*^ down to the line containing ^*) into a plain text file. On some systems you may have to give the file a name ending with ".ma" to allow Mathematica to recognize it as a Notebook. 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automaticGrouping; currentKernel; ] :[font = input; preserveAspect; startGroup] 1+1 :[font = output; output; inactive; preserveAspect; endGroup] 2 ;[o] 2 :[font = input; preserveAspect; startGroup] DG=(-w^2 +I lbd w + k); G=1/DG :[font = output; output; inactive; preserveAspect; endGroup] (k + I*lbd*w - w^2)^(-1) ;[o] 1 ---------------- 2 k + I lbd w - w :[font = input; preserveAspect] Ree[z_]:= Coefficient[Factor[ExpandAll[z]/.{Complex[0,r_]->r Iz}],Iz,0]; Ima[z_]:= Coefficient[Factor[ExpandAll[z]/.{Complex[0,r_]->r Iz}],Iz,1]; Conj[z_]:=Ree[z]-I Ima[z]; :[font = input; preserveAspect; startGroup] Ree[DG] :[font = output; output; inactive; preserveAspect; endGroup] -1 + k - w^2 ;[o] 2 -1 + k - w :[font = input; preserveAspect; startGroup] dG=D[G,w] :[font = output; output; inactive; preserveAspect; endGroup] -((I*lbd - 2*w)/(-I + k + I*lbd*w - w^2)^2) ;[o] I lbd - 2 w -(------------------------) 2 2 (-I + k + I lbd w - w ) :[font = input; preserveAspect; startGroup] Ima[dG] :[font = message; inactive; preserveAspect] General::poly: -(Iz lbd) + 2 w ----------------------------- is not a polynomial. 2 4 -1 - 2 Iz k + k + <<6>> + w :[font = output; output; inactive; preserveAspect; endGroup] Coefficient[(-(Iz*lbd) + 2*w)/ (-1 - 2*Iz*k + k^2 + 2*lbd*w + 2*Iz*k*lbd*w + 2*Iz*w^2 - 2*k*w^2 - lbd^2*w^2 - 2*Iz*lbd*w^3 + w^4), Iz, 1] ;[o] Coefficient[(-(Iz lbd) + 2 w) / 2 2 (-1 - 2 Iz k + k + 2 lbd w + 2 Iz k lbd w + 2 Iz w - 2 2 2 3 4 2 k w - lbd w - 2 Iz lbd w + w ), Iz, 1] :[font = input; preserveAspect] Solve[Im[]==0,w] :[font = input; preserveAspect; startGroup] G :[font = output; output; inactive; preserveAspect; endGroup] (-1 + k + I*lbd*w - w^2)^(-1) ;[o] 1 --------------------- 2 -1 + k + I lbd w - w :[font = input; preserveAspect; startGroup] Plot[Im[G/.{lbd->.5,k->1}],{w,0,2}] :[font = postscript; PostScript; formatAsPostScript; output; inactive; preserveAspect; pictureLeft = 34; pictureWidth = 282; pictureHeight = 174] %! %%Creator: Mathematica %%AspectRatio: .61803 MathPictureStart %% Graphics /Courier findfont 10 scalefont setfont % Scaling calculations 0.0238095 0.47619 0.603319 0.289705 [ [(0.5)] .2619 .60332 0 2 Msboxa [(1)] .5 .60332 0 2 Msboxa [(1.5)] .7381 .60332 0 2 Msboxa [(2)] .97619 .60332 0 2 Msboxa [(-2)] .01131 .02391 1 0 Msboxa [(-1.5)] .01131 .16876 1 0 Msboxa [(-1)] .01131 .31361 1 0 Msboxa [(-0.5)] .01131 .45847 1 0 Msboxa [ -0.001 -0.001 0 0 ] [ 1.001 .61903 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath [ ] 0 setdash 0 g p p .002 w .2619 .60332 m .2619 .60957 L s P [(0.5)] .2619 .60332 0 2 Mshowa p .002 w .5 .60332 m .5 .60957 L s P [(1)] .5 .60332 0 2 Mshowa p .002 w .7381 .60332 m .7381 .60957 L s P [(1.5)] .7381 .60332 0 2 Mshowa p .002 w .97619 .60332 m .97619 .60957 L s P [(2)] .97619 .60332 0 2 Mshowa p .001 w .07143 .60332 m .07143 .60707 L s P p .001 w .11905 .60332 m .11905 .60707 L s P p .001 w .16667 .60332 m .16667 .60707 L s P p .001 w .21429 .60332 m .21429 .60707 L s P p .001 w .30952 .60332 m .30952 .60707 L s P p .001 w .35714 .60332 m .35714 .60707 L s P p .001 w .40476 .60332 m .40476 .60707 L s P p .001 w .45238 .60332 m .45238 .60707 L s P p .001 w .54762 .60332 m .54762 .60707 L s P p .001 w .59524 .60332 m .59524 .60707 L s P p .001 w .64286 .60332 m .64286 .60707 L s P p .001 w .69048 .60332 m .69048 .60707 L s P p .001 w .78571 .60332 m .78571 .60707 L s P p .001 w .83333 .60332 m .83333 .60707 L s P p .001 w .88095 .60332 m .88095 .60707 L s P p .001 w .92857 .60332 m .92857 .60707 L s P p .002 w 0 .60332 m 1 .60332 L s P p .002 w .02381 .02391 m .03006 .02391 L s P [(-2)] .01131 .02391 1 0 Mshowa p .002 w .02381 .16876 m .03006 .16876 L s P [(-1.5)] .01131 .16876 1 0 Mshowa p .002 w .02381 .31361 m .03006 .31361 L s P [(-1)] .01131 .31361 1 0 Mshowa p .002 w .02381 .45847 m .03006 .45847 L s P [(-0.5)] .01131 .45847 1 0 Mshowa p .001 w .02381 .05288 m .02756 .05288 L s P p .001 w .02381 .08185 m .02756 .08185 L s P p .001 w .02381 .11082 m .02756 .11082 L s P p .001 w .02381 .13979 m .02756 .13979 L s P p .001 w .02381 .19773 m .02756 .19773 L s P p .001 w .02381 .2267 m .02756 .2267 L s P p .001 w .02381 .25567 m .02756 .25567 L s P p .001 w .02381 .28464 m .02756 .28464 L s P p .001 w .02381 .34258 m .02756 .34258 L s P p .001 w .02381 .37156 m .02756 .37156 L s P p .001 w .02381 .40053 m .02756 .40053 L s P p .001 w .02381 .4295 m .02756 .4295 L s P p .001 w .02381 .48744 m .02756 .48744 L s P p .001 w .02381 .51641 m .02756 .51641 L s P p .001 w .02381 .54538 m .02756 .54538 L s P p .001 w .02381 .57435 m .02756 .57435 L s P p .002 w .02381 0 m .02381 .61803 L s P P 0 0 m 1 0 L 1 .61803 L 0 .61803 L closepath clip newpath p p .004 w .02381 .60332 m .06349 .5911 L .10317 .57796 L .14286 .56284 L .18254 .54428 L .22222 .52022 L .2619 .48744 L .30159 .44092 L .32143 .41028 L .34127 .37326 L .38095 .27612 L .42063 .15118 L .44048 .0888 L .4504 .0618 L .46032 .03968 L .46528 .03094 L .47024 .02395 L .47272 .02116 L .4752 .01885 L .47768 .01705 L .47892 .01634 L .48016 .01576 L .4814 .0153 L .48264 .01498 L .48388 .01478 L .48512 .01472 L .48636 .01478 L .4876 .01497 L .48884 .0153 L .49008 .01575 L .49256 .01704 L .49504 .01884 L .5 .02391 L .50496 .03087 L .50992 .03957 L .51984 .06154 L .53968 .1183 L .57937 .24428 L .59921 .29981 L .61905 .34723 L .63889 .38673 L .65873 .41927 L .67857 .44598 L .69841 .46793 L .71825 .48604 L .7381 .50107 L .77778 .52417 L .81746 .54069 L .85714 .55282 L .89683 .56192 L Mistroke .93651 .5689 L .97619 .57435 L Mfstroke P P % End of Graphics MathPictureEnd :[font = output; 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