(*^
::[	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.
	The line below identifies what version of Mathematica created this file,
	but it can be opened using any other version as well.";

	FrontEndVersion = "Macintosh Mathematica Notebook Front End Version 2.2";

	MacintoshStandardFontEncoding; 
	
	fontset = title, inactive, noPageBreakBelow, nohscroll, preserveAspect, groupLikeTitle, center, M7, bold, e8,  24, "Times"; 
	fontset = subtitle, inactive, noPageBreakBelow, nohscroll, preserveAspect, groupLikeTitle, center, M7, bold, e6,  18, "Times"; 
	fontset = subsubtitle, inactive, noPageBreakBelow, nohscroll, preserveAspect, groupLikeTitle, center, M7, italic, e6,  14, "Times"; 
	fontset = section, inactive, noPageBreakBelow, nohscroll, preserveAspect, groupLikeSection, grayBox, M22, bold, a20,  18, "Times"; 
	fontset = subsection, inactive, noPageBreakBelow, nohscroll, preserveAspect, groupLikeSection, blackBox, M19, bold, a15,  14, "Times"; 
	fontset = subsubsection, inactive, noPageBreakBelow, nohscroll, preserveAspect, groupLikeSection, whiteBox, M18, bold, a12,  12, "Times"; 
	fontset = text, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7,  12, "Times"; 
	fontset = smalltext, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7,  10, "Times"; 
	fontset = input, noPageBreakInGroup, nowordwrap, preserveAspect, groupLikeInput, M42, N23, bold, L-5,  12, "Courier"; 
	fontset = output, output, inactive, noPageBreakInGroup, nowordwrap, preserveAspect, groupLikeOutput, M42, N23, L-5,  12, "Courier"; 
	fontset = message, inactive, noPageBreakInGroup, nowordwrap, preserveAspect, groupLikeOutput, M42, N23, R65535, L-5,  12, "Courier"; 
	fontset = print, inactive, noPageBreakInGroup, nowordwrap, preserveAspect, groupLikeOutput, M42, N23, L-5,  12, "Courier"; 
	fontset = info, inactive, noPageBreakInGroup, nowordwrap, preserveAspect, groupLikeOutput, M42, N23, B65535, L-5,  12, "Courier"; 
	fontset = postscript, PostScript, formatAsPostScript, output, inactive, noPageBreakInGroup, nowordwrap, preserveAspect, groupLikeGraphics, M7, l34, w282, h287,  12, "Courier"; 
	fontset = name, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7, italic,  10, "Geneva"; 
	fontset = header, inactive, noKeepOnOnePage, preserveAspect, M7,  12, "Times"; 
	fontset = leftheader, inactive, L2,  12, "Times"; 
	fontset = footer, inactive, noKeepOnOnePage, preserveAspect, center, M7,  12, "Times"; 
	fontset = leftfooter, inactive, L2,  12, "Times"; 
	fontset = help, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7,  10, "Times"; 
	fontset = clipboard, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7,  12, "Times"; 
	fontset = completions, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7,  12, "Times"; 
	fontset = special1, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7,  12, "Times"; 
	fontset = special2, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7,  12, "Times"; 
	fontset = special3, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7,  12, "Times"; 
	fontset = special4, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7,  12, "Times"; 
	fontset = special5, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7,  12, "Times"; 
	paletteColors = 128; currentKernel; 
]
:[font = title; inactive; noPageBreak; preserveAspect]
Homework 6:
:[font = input; noPageBreak; preserveAspect]
Needs["Algebra`Trigonometry`"]

:[font = input; noPageBreak; preserveAspect]
conjugate::usage = 
" A simple method of computing the conjugate of an object
 which is explicitly Complex";

conjugateRule     = {Complex[re_,im_]:>Complex[re,-im]};
conjugate[exp__] := exp /. conjugateRule;
:[font = title; inactive; noPageBreak; preserveAspect; cellOutline; backColorRed = 58981; backColorGreen = 58981; backColorBlue = 58981]
Not complete: 
You must fill in missing steps:
:[font = section; inactive; noPageBreak; preserveAspect; startGroup]
Problem 1:
:[font = input; noPageBreak; preserveAspect]
Clear["Global`*"];
:[font = subsection; inactive; noPageBreak; preserveAspect]
Part a)
:[font = input; noPageBreak; preserveAspect]
(* Replace: w0^2 = k/m *)

mSol= Solve[w0^2 == k/m ,m][[1]]
:[font = input; noPageBreak; preserveAspect]
eq1= m x''[t] + k x[t] == 0 /.mSol
:[font = input; noPageBreak; preserveAspect]
dSol= DSolve[eq1,x,t][[1]];
{x[t], x'[t], x''[t]} /.dSol //TableForm
:[font = subsection; inactive; noPageBreak; preserveAspect]
Part b) 
I'll do this in general first.
:[font = input; noPageBreak; preserveAspect]
{position,velocity,acceleration}= 
     {x[t], x'[t], x''[t]} /.dSol  //ComplexToTrig //Simplify
:[font = input; noPageBreak; preserveAspect]
Plot[{position,velocity,acceleration} /.{w0->2} //Evaluate
    ,{t,0, 2 Pi}
    ,PlotStyle->{{},{Dashing[{0.020}]},{Thickness[0.008]}}
    ];
:[font = section; inactive; noPageBreak; preserveAspect]
Part c)
:[font = input; noPageBreak; preserveAspect]
{kinetic, potential, total} = 
 {1/2 m velocity^2 , 1/2 k position^2, 
  1/2 m velocity^2 + 1/2 k position^2} 
:[font = input; noPageBreak; preserveAspect]
Plot[{kinetic, potential, total} /.{w0->2, k->4} //Evaluate
    ,{t,0, 2 Pi}
    ,PlotStyle->{{},{Dashing[{0.020}]},{Thickness[0.008]}}
    ];
:[font = section; inactive; noPageBreak; preserveAspect]
Part d)
:[font = input; noPageBreak; preserveAspect; endGroup]
ParametricPlot[{position,velocity} /.{w0->2} //Evaluate
            ,{t,0, 2 Pi}];
:[font = section; inactive; noPageBreak; preserveAspect; startGroup]
Problem 4:
:[font = input; noPageBreak; preserveAspect]
Clear["Global`*"];
:[font = subsection; inactive; noPageBreak; preserveAspect]
Part a)
:[font = input; noPageBreak; preserveAspect]
(* Short cut: Don't put in the "==" yet. *)

eq1= L q''[t] + R q'[t] + 1/C q[t] - e0 Exp[I w t]
:[font = input; noPageBreak; preserveAspect]
eq2= D[eq1,t] 
:[font = input; noPageBreak; preserveAspect]
(* Use c for current: *)

qRule= {q-> (Integrate[c[#],#]&) }
:[font = input; noPageBreak; preserveAspect]
{q[t], q'[t], q''[t], q'''[t]} /.qRule
:[font = subsection; inactive; noPageBreak; preserveAspect]
Part e)
:[font = input; noPageBreak; preserveAspect]
values= {L->L0, C -> 300 10^-12, R ->5, w0-> 2 Pi 10^4};
:[font = input; noPageBreak; preserveAspect; endGroup]
mag= impedance (impedance //conjugate) //Simplify
:[font = section; inactive; noPageBreak; preserveAspect; startGroup]
Problem 5:
:[font = input; noPageBreak; preserveAspect]
Clear["Global`*"];
:[font = subsection; inactive; noPageBreak; preserveAspect]
Part a)
:[font = input; noPageBreak; preserveAspect; endGroup]
Plot[({x1[t],x2[t],x3[t]} //Re)  //Evaluate 
    ,{t,0,20}
    ,PlotStyle->{{},{Dashing[{0.020}]},{Thickness[0.008]}}
    ];
:[font = section; inactive; noPageBreak; preserveAspect; startGroup]
Problem 6:
:[font = input; noPageBreak; preserveAspect]
Clear["Global`*"];
:[font = subsection; inactive; noPageBreak; preserveAspect]
Part a)
:[font = input; noPageBreak; preserveAspect]
fun[c0_,c1_,c2_,c3_]:= 
 ( c0 
 + c1 Sin[2 Pi 1 x]
 + c2 Sin[2 Pi 2 x]
 + c3 Sin[2 Pi 3 x]
 )
:[font = input; noPageBreak; preserveAspect]
doit[c0_,c1_,c2_,c3_]:= Plot[ fun[c0,c1,c2,c3] //Evaluate ,{x,0,1}];
:[font = input; noPageBreak; preserveAspect; endGroup]
doit[1,2,3,4];
:[font = section; inactive; noPageBreak; preserveAspect; startGroup]
Problem 7:
:[font = input; noPageBreak; preserveAspect]
Clear["Global`*"];
:[font = subsection; inactive; noPageBreak; preserveAspect]
Part a)
:[font = input; noPageBreak; preserveAspect; endGroup]
Plot[Ceiling[x+1/2],{x,0,1}];
:[font = section; inactive; noPageBreak; preserveAspect; startGroup]
Problem 8:
:[font = input; noPageBreak; preserveAspect]
Clear["Global`*"];
:[font = subsection; inactive; noPageBreak; preserveAspect]
Part a)
:[font = input; noPageBreak; preserveAspect; endGroup]
Plot[1-Abs[x],{x,-1,1}];
^*)