{VERSION 6 0 "IBM INTEL NT" "6.0" }
{USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 
1 0 0 0 0 1 }{CSTYLE "" -1 256 "" 1 14 0 0 0 0 0 1 1 0 0 0 0 0 0 0 }
{CSTYLE "" -1 257 "" 1 24 0 0 0 0 0 1 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 
258 "" 0 1 0 0 0 0 0 1 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 260 "" 1 18 0 0 
0 0 1 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 261 "" 1 18 0 0 0 0 0 0 0 0 0 
0 0 0 0 0 }{CSTYLE "" -1 265 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }
{CSTYLE "" -1 266 "" 1 18 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 
267 "" 1 18 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 268 "" 1 18 0 
0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 269 "" 1 18 0 0 0 0 1 1 0 0 
0 0 0 0 0 0 }{CSTYLE "" -1 270 "" 1 18 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }
{CSTYLE "" -1 271 "" 1 18 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 
272 "" 1 18 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 273 "" 1 18 0 
0 0 0 0 1 0 0 0 0 0 0 0 0 }{PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "T
imes" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 }
{PSTYLE "Normal" -1 256 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 
2 2 2 1 1 1 1 }3 1 0 0 0 0 1 0 1 0 2 2 0 1 }}
{SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "
> " 0 "" {MPLTEXT 1 0 21 "restart: with(plots):" }}}{EXCHG {PARA 256 "
" 0 "" {TEXT 258 0 "" }{TEXT 256 0 "" }{TEXT 257 46 "PH221:  Introduct
ion to Superposition Activity" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}
{PARA 0 "" 0 "" {TEXT -1 0 "" }{TEXT 260 13 "Superposition" }{TEXT 
261 649 " is one of the most fundamaental and crucial physical aspects
 of our studies, playing a part in Classical Mechanics, Electromagneti
cs, Optics, Quantum Mechanics, and Statistical Mechanics alike.  Super
position is our approach to dealing with multiple phenomena (of the sa
me kind) with the same spatial and temporal conditions mixing together
.  Essentially, superposition says that when two oscillatory functions
 (Classical Mechanics, E&M) or states (Quantum Mechanics, Statistical \+
Mechanics) are imparted at the same place and time, the resulting osci
llation, or state, will be the sum of the two added together.  Let's b
uild on some simple cases..." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 
0 "" 0 "" {TEXT -1 0 "" }{TEXT 265 0 "" }{TEXT 266 100 "On your small \+
white boards, plot the superposition of the following oscillations in \+
the time domain:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "f:= sin
(Pi*t);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "g:= 3*sin(Pi*t);
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 38 "plot([f,g],t=0..2*Pi,th
ickness=[3,3]);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 62 "plot([f+
g,f,g],t=0..2*Pi,thickness=[3,1,1],linestyle=[1,3,3]);" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "h:= -f;" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 38 "plot([f,h],t=0..2*Pi,thickness=[3,3]);" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 62 "plot([f+h,f,h],t=0..2*Pi,thickness=
[3,1,1],linestyle=[1,3,3]);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
14 "a:= cos(Pi*t);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 38 "plot(
[f,a],t=0..2*Pi,thickness=[3,3]);" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 62 "plot([f+a,f,a],t=0..2*Pi,thickness=[3,1,1],linestyle=
[1,3,3]);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }{TEXT 267 0 "" }
{TEXT 268 62 "So far, we have been looking at sinusoidal functions wit
h the " }{TEXT 269 14 "same frequency" }{TEXT 270 109 ".  Let's see wh
at happens if we take the superposition of oscillating functions with \+
different frequencies..." }{TEXT 271 0 "" }{TEXT -1 0 "" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "b:= sin(2*Pi*t);" }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 38 "plot([f,b],t=0..2*Pi,thickness=[3,3]);" }
}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 62 "plot([f+b,f,b],t=0..2*Pi,t
hickness=[3,1,1],linestyle=[1,3,3]);" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 16 "c:= sin(Pi*t/5);" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 38 "plot([f,c],t=0..4*Pi,thickness=[3,3]);" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 62 "plot([f+c,f,c],t=0..4*Pi,thickness=
[3,1,1],linestyle=[1,3,3]);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
21 "d:= sin(Pi*t/(5^.5));" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
38 "plot([f,d],t=0..4*Pi,thickness=[3,3]);" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 63 "plot([f+d,f,d],t=0..12*Pi,thickness=[3,1,1],linesty
le=[1,3,3]);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }{TEXT 272 0 "" 
}{TEXT 273 186 "Now that you've plotted some of these functios by hand
 and seen some others plotted for you, plot the superposition fo one m
ore set of oscillating functions on your small white boards..." }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 232 "a:= 2*sin(t)/Pi; b:=2*sin(3
*t)/(3*Pi); c:= 2*sin(5*t)/(5*Pi); d:= 2*sin(7*t)/(7*Pi); f:= 2*sin(9*
t)/(9*Pi); g:= 2*sin(11*t)/(11*Pi); h:= 2*sin(13*t)/(13*Pi); j:= 2*sin
(15*t)/(15*Pi); k:= 2*sin(17*t)/(17*Pi); l:= 2*sin(19*t)/(19*Pi);" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "s:= a+b+c+d+f+g+h+j+k+l;" }}
}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "plot(s,t=0..4*Pi,thickness=
3);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 67 "Nsum:= 20; fs(t):=1/
2+2/Pi*Sum(1/(2*m+1)*sin((2*m+1)*t),m=0..Nsum);" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 55 "sq(t):=piecewise(t<=-Pi, 1, t<0, 0, t<=Pi, 1, \+
t>Pi, 0);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 62 "plot([sq(t),fs
(t)],t=-2*Pi..2*Pi,axes=normal,thickness=[2,2]);" }}}{EXCHG {PARA 0 ">
 " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "31" 0 }{VIEWOPTS 1 1 0 1 1 1803 
1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }