{VERSION 6 1 "Windows XP" "6.1" }
{USTYLETAB {PSTYLE "Dash Item" -1 16 1 {CSTYLE "" -1 -1 "Times" 1 12 
0 0 0 1 2 2 2 2 2 2 0 0 0 1 }1 1 0 0 3 3 2 0 2 0 2 2 -1 3 }{PSTYLE "Wa
rning" -1 7 1 {CSTYLE "" -1 -1 "Courier" 1 10 0 0 255 1 0 0 0 2 2 1 0 
0 0 1 }1 0 0 -1 -1 -1 1 0 1 0 2 2 -1 1 }{PSTYLE "Normal259" -1 200 1 
{CSTYLE "" -1 -1 "Times" 1 24 0 0 0 1 2 2 2 2 2 2 0 0 0 1 }1 1 0 0 0 
0 2 0 2 0 2 2 -1 1 }{PSTYLE "Bullet Item" -1 15 1 {CSTYLE "" -1 -1 "Ti
mes" 1 12 0 0 0 1 2 2 2 2 2 2 0 0 0 1 }1 1 0 0 3 3 2 0 2 0 2 2 -1 2 }
{PSTYLE "Normal258" -1 201 1 {CSTYLE "" -1 -1 "Times" 1 24 0 0 0 1 2 
2 2 2 2 2 0 0 0 1 }3 1 0 0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "Normal257" 
-1 202 1 {CSTYLE "" -1 -1 "Times" 1 14 0 0 0 1 2 2 2 2 2 2 0 0 0 1 }3 
1 0 0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "Line Printed Output" -1 6 1 
{CSTYLE "" -1 -1 "Courier" 1 10 0 0 255 1 0 0 0 2 2 1 0 0 0 1 }1 0 0 
-1 -1 -1 1 0 1 0 2 2 -1 1 }{PSTYLE "Heading 4" -1 20 1 {CSTYLE "" -1 
-1 "Times" 1 10 0 0 0 1 1 1 2 2 2 2 0 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 2 
-1 1 }{PSTYLE "Heading 3" -1 5 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 
1 1 1 2 2 2 2 0 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "Heading \+
2" -1 4 1 {CSTYLE "" -1 -1 "Times" 1 14 0 0 0 1 2 1 2 2 2 2 0 0 0 1 }
1 1 0 0 8 2 2 0 2 0 2 2 -1 1 }{PSTYLE "Maple Output" -1 11 1 {CSTYLE "
" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 0 0 0 1 }3 3 0 0 0 0 2 0 2 0 
2 2 -1 1 }{PSTYLE "Heading 1" -1 3 1 {CSTYLE "" -1 -1 "Times" 1 18 0 
0 0 1 2 1 2 2 2 2 0 0 0 1 }1 1 0 0 8 4 2 0 2 0 2 2 -1 1 }{PSTYLE "Auth
or" -1 19 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 0 0 0 1 
}3 1 0 0 8 8 2 0 2 0 2 2 -1 1 }{PSTYLE "Maple Plot" -1 13 1 {CSTYLE ""
 -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 0 0 0 1 }3 1 0 0 0 0 2 0 2 0 
2 2 -1 1 }{PSTYLE "Help" -1 10 1 {CSTYLE "" -1 -1 "Courier" 1 9 0 0 
255 1 0 0 0 2 2 1 0 0 0 1 }1 0 0 -1 -1 -1 1 0 1 0 2 2 -1 1 }{PSTYLE "L
eft Justified Maple Output" -1 12 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 
0 1 2 2 2 2 2 2 0 0 0 1 }1 3 0 0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "Fixed \+
Width" -1 17 1 {CSTYLE "" -1 -1 "Courier" 1 10 0 0 0 1 2 2 2 2 2 2 0 
0 0 1 }3 1 0 0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "Text Output" -1 2 1 
{CSTYLE "" -1 -1 "Courier" 1 10 0 0 255 1 0 0 0 2 2 1 0 0 0 1 }1 0 0 
-1 -1 -1 1 0 1 0 2 2 -1 1 }{PSTYLE "List Item" -1 14 1 {CSTYLE "" -1 
-1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 0 0 0 1 }1 1 0 0 3 3 2 0 2 0 2 2 
-1 5 }{PSTYLE "Error" -1 8 1 {CSTYLE "" -1 -1 "Courier" 1 10 255 0 
255 1 0 0 0 2 2 1 0 0 0 1 }1 0 0 -1 -1 -1 1 0 1 0 2 2 -1 1 }{PSTYLE "D
iagnostic" -1 9 1 {CSTYLE "" -1 -1 "Courier" 1 10 64 128 64 1 0 0 0 2 
2 1 0 0 0 1 }1 0 0 -1 -1 -1 1 0 1 0 2 2 -1 1 }{PSTYLE "Title" -1 18 1 
{CSTYLE "" -1 -1 "Times" 1 18 0 0 0 1 2 1 1 2 2 2 0 0 0 1 }3 1 0 0 12 
12 2 0 2 0 2 2 -1 1 }{PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "Times" 
1 14 0 0 0 1 2 2 2 2 2 2 0 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }
{PSTYLE "MyWork" -1 203 1 {CSTYLE "" -1 -1 "Times" 1 14 0 0 0 1 2 2 2 
2 2 2 0 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "Normal260" -1 
204 1 {CSTYLE "" -1 -1 "Times" 1 18 0 0 0 1 2 2 2 2 2 2 0 0 0 1 }1 1 
0 0 0 0 2 0 2 0 2 2 -1 1 }{CSTYLE "LaTeX" -1 32 "" 0 1 0 0 0 0 0 0 0 
2 2 2 0 0 0 1 }{CSTYLE "Maple Comment" -1 21 "Courier" 0 1 0 0 0 1 0 
0 0 2 2 2 0 0 0 1 }{CSTYLE "2D Math Bold" -1 5 "Times" 0 1 0 0 0 0 0 
1 2 2 2 2 0 0 0 1 }{CSTYLE "Help Underlined" -1 44 "Times" 1 12 0 0 0 
0 0 0 1 2 2 2 0 0 0 1 }{CSTYLE "Output Labels" -1 29 "Times" 1 8 0 0 
0 1 0 0 0 2 2 2 0 0 0 1 }{CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 
0 0 1 0 1 0 2 1 2 0 0 0 1 }{CSTYLE "Page Number" -1 33 "Times" 0 1 0 
0 0 0 0 0 2 2 2 2 0 0 0 1 }{CSTYLE "Maple Input Placeholder" -1 200 "C
ourier" 1 12 200 0 200 1 0 1 0 2 1 2 0 0 0 1 }{CSTYLE "Text" -1 201 "T
imes" 1 12 0 0 0 1 2 2 2 2 2 2 0 0 0 1 }{CSTYLE "2D Math Italic Small"
 -1 202 "Times" 0 1 0 0 0 0 1 0 2 2 2 2 0 0 0 1 }{CSTYLE "Help Heading
" -1 26 "" 1 14 0 0 0 0 0 1 0 2 2 2 0 0 0 1 }{CSTYLE "Help Italic Bold
" -1 40 "Times" 1 12 0 0 0 0 1 1 0 2 2 2 0 0 0 1 }{CSTYLE "Help Normal
" -1 30 "Times" 1 12 0 0 0 0 0 0 0 2 2 2 0 0 0 1 }{CSTYLE "Help Nonter
minal" -1 24 "Courier" 0 1 0 0 0 1 0 1 0 2 2 2 0 0 0 1 }{CSTYLE "2D Ma
th Small" -1 7 "Times" 0 1 0 0 0 0 0 0 2 2 2 2 0 0 0 1 }{CSTYLE "Help \+
Underlined Italic" -1 43 "Times" 1 12 0 0 0 0 1 0 1 2 2 2 0 0 0 1 }
{CSTYLE "2D Math" -1 2 "Times" 0 1 0 0 0 0 0 0 2 2 2 2 0 0 0 1 }
{CSTYLE "Copyright" -1 34 "Times" 1 10 0 0 0 0 2 2 2 2 2 2 0 0 0 1 }
{CSTYLE "Hyperlink" -1 17 "" 0 1 0 128 128 1 2 0 1 2 2 2 0 0 0 1 }
{CSTYLE "Plot Title" -1 27 "" 1 10 0 0 0 0 0 1 0 2 2 2 0 0 0 1 }
{CSTYLE "2D Input" -1 19 "Times" 0 1 255 0 0 1 0 0 2 2 1 2 0 0 0 1 }
{CSTYLE "Help Maple Name" -1 35 "" 0 1 104 64 92 1 0 1 0 2 2 2 0 0 0 
1 }{CSTYLE "Help Italic" -1 42 "Times" 1 12 0 0 0 0 1 0 0 2 2 2 0 0 0 
1 }{CSTYLE "Help Underlined Bold" -1 41 "Times" 1 12 0 0 0 0 0 1 1 2 
2 2 0 0 0 1 }{CSTYLE "Default" -1 38 "" 0 1 0 0 0 0 0 0 0 2 2 2 0 0 0 
1 }{CSTYLE "Help Fixed" -1 23 "Courier" 1 10 0 0 0 0 0 0 0 2 2 2 0 0 
0 1 }{CSTYLE "_cstyle264" -1 203 "" 0 1 0 0 0 0 0 1 0 2 2 2 0 0 0 1 }
{CSTYLE "_cstyle263" -1 204 "" 0 1 0 0 0 0 0 1 0 2 2 2 0 0 0 1 }
{CSTYLE "_cstyle262" -1 205 "" 0 1 0 0 0 0 0 1 0 2 2 2 0 0 0 1 }
{CSTYLE "Dictionary Hyperlink" -1 45 "" 0 1 147 0 15 1 2 0 1 2 2 2 0 
0 0 1 }{CSTYLE "_cstyle261" -1 206 "" 0 1 0 0 0 0 0 1 0 2 2 2 0 0 0 1 
}{CSTYLE "2D Output" -1 20 "Times" 0 1 0 0 255 1 0 0 2 2 2 2 0 0 0 1 }
{CSTYLE "_cstyle260" -1 207 "" 0 1 0 0 0 0 0 1 0 2 2 2 0 0 0 1 }
{CSTYLE "2D Math Italic" -1 3 "Times" 0 1 0 0 0 0 1 0 2 2 2 2 0 0 0 1 
}{CSTYLE "Popup" -1 31 "" 0 1 0 128 128 1 1 0 1 2 2 2 0 0 0 1 }
{CSTYLE "2D Math Symbol 2" -1 16 "Times" 0 1 0 0 0 0 2 2 2 2 2 2 0 0 
0 1 }{CSTYLE "Plot Text" -1 28 "" 1 8 0 0 0 0 0 0 0 2 2 2 0 0 0 1 }
{CSTYLE "Help Notes" -1 37 "" 0 1 0 0 0 1 0 1 0 2 2 2 0 0 0 1 }
{CSTYLE "Help Bold" -1 39 "Times" 1 12 0 0 0 0 0 1 0 2 2 2 0 0 0 1 }
{CSTYLE "Help Menus" -1 36 "" 0 1 0 0 0 1 0 1 0 2 2 2 0 0 0 1 }
{CSTYLE "_cstyle259" -1 208 "" 1 24 0 0 0 0 0 0 0 2 2 2 0 0 0 1 }
{CSTYLE "_cstyle258" -1 209 "" 1 15 0 0 0 0 0 0 0 2 2 2 0 0 0 1 }
{CSTYLE "_cstyle257" -1 210 "" 0 1 0 0 0 0 0 1 0 2 2 2 0 0 0 1 }
{CSTYLE "_cstyle256" -1 211 "" 0 1 0 0 0 0 0 1 0 2 2 2 0 0 0 1 }
{CSTYLE "2D Comment" -1 18 "Times" 0 1 0 0 0 0 0 0 2 2 2 2 0 0 0 1 }
{CSTYLE "Help Variable" -1 25 "Courier" 0 1 0 0 0 1 2 2 0 2 2 2 0 0 0 
1 }{CSTYLE "2D Math Bold Small" -1 10 "Times" 0 1 0 0 0 0 0 1 2 2 2 2 
0 0 0 1 }{CSTYLE "Help Emphasized" -1 212 "" 0 1 0 0 0 0 1 2 0 2 2 2 
0 0 0 1 }{CSTYLE "Prompt" -1 1 "Courier" 0 1 0 0 0 1 0 0 0 2 2 2 0 0 
0 1 }{PSTYLE "_pstyle1" -1 205 1 {CSTYLE "" -1 -1 "Times" 1 14 0 0 0 
1 2 2 2 2 2 2 1 0 0 1 }3 1 0 0 0 0 2 0 2 0 2 2 -1 1 }{CSTYLE "_cstyle1
" -1 213 "Times" 1 14 0 0 0 1 2 2 2 2 2 2 0 0 0 1 }{PSTYLE "_pstyle2" 
-1 206 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 1 0 2 2 2 1 0 0 1 }3 1 0 0 
0 0 2 0 2 0 2 2 -1 1 }{CSTYLE "_cstyle2" -1 214 "Times" 1 24 0 0 0 1 
2 1 2 2 2 2 0 0 0 1 }{PSTYLE "_pstyle3" -1 207 1 {CSTYLE "" -1 -1 "Tim
es" 1 24 0 0 0 1 2 2 2 2 2 2 1 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }
{CSTYLE "_cstyle3" -1 215 "Times" 1 24 0 0 0 1 2 2 2 2 2 2 0 0 0 1 }
{PSTYLE "_pstyle4" -1 208 1 {CSTYLE "" -1 -1 "Times" 1 14 0 0 0 1 2 2 
2 2 2 2 1 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }{CSTYLE "_cstyle4" -1 
216 "Times" 1 15 0 0 0 1 2 2 2 2 2 2 0 0 0 1 }{CSTYLE "_cstyle5" -1 
217 "Times" 1 24 0 0 0 1 2 2 2 2 2 2 0 0 0 1 }{CSTYLE "_cstyle6" -1 
218 "Times" 1 14 0 0 0 1 2 2 2 2 2 2 0 0 0 1 }{PSTYLE "_pstyle5" -1 
209 1 {CSTYLE "" -1 -1 "Courier" 0 1 255 0 0 1 0 1 0 2 1 2 1 0 0 1 }1 
1 0 0 0 0 2 0 2 0 2 2 -1 1 }{CSTYLE "_cstyle7" -1 219 "Courier" 1 14 
255 0 0 1 2 1 2 2 1 2 0 0 0 1 }{PSTYLE "_pstyle6" -1 210 1 {CSTYLE "" 
-1 -1 "" 0 1 0 0 0 0 0 1 0 2 2 2 1 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 
1 }{CSTYLE "_cstyle8" -1 220 "Times" 1 14 0 0 0 1 2 1 2 2 2 2 0 0 0 1 
}{PSTYLE "_pstyle7" -1 211 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 1 0 2 
2 2 1 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }{CSTYLE "_cstyle9" -1 221 "
Times" 1 14 0 0 0 1 2 1 2 2 2 2 0 0 0 1 }{CSTYLE "_cstyle10" -1 222 "T
imes" 1 14 0 0 0 1 2 1 2 2 2 2 0 0 0 1 }{PSTYLE "_pstyle8" -1 212 1 
{CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 1 0 2 2 2 1 0 0 1 }1 1 0 0 0 0 2 0 
2 0 2 2 -1 1 }{CSTYLE "_cstyle11" -1 223 "Times" 1 14 0 0 0 1 2 1 2 2 
2 2 0 0 0 1 }{CSTYLE "_cstyle12" -1 224 "Courier" 0 1 255 0 0 1 0 1 0 
2 1 2 0 0 0 1 }{PSTYLE "_pstyle9" -1 213 1 {CSTYLE "" -1 -1 "" 0 1 0 
0 0 0 0 0 0 2 2 2 0 0 0 1 }0 0 0 -1 -1 -1 1 0 1 0 2 2 -1 1 }}
{SECT 0 {EXCHG {PARA 205 "" 0 "" {TEXT 213 0 "" }}{PARA 206 "" 0 "" 
{TEXT 214 18 "FORCED  VIBRATIONS" }{TEXT 214 0 "" }}{PARA 207 "" 0 "" 
{TEXT 215 16 "                " }{TEXT 215 0 "" }}{PARA 208 "" 0 "" 
{TEXT 216 68 "                                                        \+
            " }{TEXT 217 30 "mu'' + cu' + ku = F0 cos(w t)," }{TEXT 
218 0 "" }}{PARA 208 "" 0 "" {TEXT 218 0 "" }}}{EXCHG {PARA 209 "> " 0
 "" {MPLTEXT 1 219 8 "restart;" }{MPLTEXT 1 219 0 "" }}}{EXCHG {PARA 
208 "" 0 "" {TEXT 218 0 "" }}{PARA 208 "" 0 "" {TEXT 218 11 "No Dampin
g:" }{TEXT 218 0 "" }}{PARA 208 "" 0 "" {TEXT 218 0 "" }}}{EXCHG 
{PARA 209 "> " 0 "" {MPLTEXT 1 219 43 "MS:=diff(u(t),t$2) + w0^2*u(t)=
 F*cos(w*t);" }{MPLTEXT 1 219 0 "" }}}{EXCHG {PARA 209 "> " 0 "" 
{MPLTEXT 1 219 29 "eq1:=subs(\{w=2,w0=4,F=4\},MS);" }{MPLTEXT 1 219 0 
"" }}}{EXCHG {PARA 208 "" 0 "" {TEXT 218 0 "" }}{PARA 208 "" 0 "" 
{TEXT 218 17 "General solution:" }{TEXT 218 0 "" }}{PARA 208 "" 0 "" 
{TEXT 218 0 "" }}}{EXCHG {PARA 209 "> " 0 "" {MPLTEXT 1 219 17 "dsolve
(eq1,u(t));" }{MPLTEXT 1 219 0 "" }}}{EXCHG {PARA 208 "" 0 "" {TEXT 
218 0 "" }}{PARA 208 "" 0 "" {TEXT 218 19 "Initial conditions:" }
{TEXT 218 0 "" }}{PARA 208 "" 0 "" {TEXT 218 0 "" }}}{EXCHG {PARA 209 
"> " 0 "" {MPLTEXT 1 219 13 "u0:=1; v0:=1;" }{MPLTEXT 1 219 0 "" }}}
{EXCHG {PARA 209 "> " 0 "" {MPLTEXT 1 219 39 "dsolve(\{eq1, u(0)=u0,D(
u)(0)=v0\},u(t));" }{MPLTEXT 1 219 0 "" }}}{EXCHG {PARA 209 "> " 0 "" 
{MPLTEXT 1 219 47 "S:=rhs(dsolve(\{eq1, u(0)=u0,D(u)(0)=v0\},u(t)));" 
}{MPLTEXT 1 219 0 "" }}}{EXCHG {PARA 209 "> " 0 "" {MPLTEXT 1 219 17 "
u1:=unapply(S,t);" }{MPLTEXT 1 219 0 "" }}}{EXCHG {PARA 209 "> " 0 "" 
{MPLTEXT 1 219 21 "plot(u1(t), t=0..10);" }{MPLTEXT 1 219 0 "" }}}
{EXCHG {PARA 208 "" 0 "" {TEXT 218 0 "" }}{PARA 210 "" 0 "" {TEXT 220 
18 "RESONANCE (W = W0)" }{TEXT 220 0 "" }}{PARA 208 "" 0 "" {TEXT 218 
0 "" }}}{EXCHG {PARA 209 "> " 0 "" {MPLTEXT 1 219 29 "eq2:=subs(\{w=2,
w0=2,F=4\},MS);" }{MPLTEXT 1 219 0 "" }}}{EXCHG {PARA 209 "> " 0 "" 
{MPLTEXT 1 219 70 "u2:=unapply(combine(rhs(dsolve(\{eq2,D(u)(0)=1,u(0)
=1\},u(t))),trig),t);" }{MPLTEXT 1 219 0 "" }}}{EXCHG {PARA 209 "> " 0
 "" {MPLTEXT 1 219 21 "plot(u2(t), t=0..30);" }{MPLTEXT 1 219 0 "" }}}
{EXCHG {PARA 208 "" 0 "" {TEXT 218 0 "" }}{PARA 211 "" 0 "" {TEXT 221 
25 "Beats ( |w-w0| < epsilon)" }{TEXT 221 0 "" }}{PARA 208 "" 0 "" 
{TEXT 218 0 "" }}}{EXCHG {PARA 209 "> " 0 "" {MPLTEXT 1 219 34 "eq3:= \+
subs(\{w=21/10,w0=2,F=4\},MS);" }{MPLTEXT 1 219 0 "" }}}{EXCHG {PARA 
209 "> " 0 "" {MPLTEXT 1 219 70 "u3:=unapply(combine(rhs(dsolve(\{eq3,
D(u)(0)=1,u(0)=1\},u(t))),trig),t);" }{MPLTEXT 1 219 0 "" }}}{EXCHG 
{PARA 209 "> " 0 "" {MPLTEXT 1 219 22 "plot(u3(t), t=0..130);" }
{MPLTEXT 1 219 0 "" }}}{EXCHG {PARA 208 "" 0 "" {TEXT 218 0 "" }}
{PARA 208 "" 0 "" {TEXT 222 32 "FORCED VIBRATIONS WITH DAMPING (" }
{TEXT 218 10 "C NON NULL" }{TEXT 222 1 ")" }{TEXT 218 0 "" }}{PARA 
208 "" 0 "" {TEXT 218 0 "" }}}{EXCHG {PARA 209 "> " 0 "" {MPLTEXT 1 
219 63 "MSF:=diff(u(t),t$2) + 2*b*diff(u(t),t) + w0^2*u(t)= F*cos(w*t)
;" }{MPLTEXT 1 219 0 "" }}}{EXCHG {PARA 209 "> " 0 "" {MPLTEXT 1 219 
38 "MSF1:=subs(\{w=2,w0=4,b=1/12,F=4\},MSF);" }{MPLTEXT 1 219 0 "" }}}
{EXCHG {PARA 209 "> " 0 "" {MPLTEXT 1 219 59 "u1f:= unapply(rhs(dsolve
(\{MSF1,D(u)(0)=1,u(0)=1\},u(t))),t);" }{MPLTEXT 1 219 0 "" }}}{EXCHG 
{PARA 209 "> " 0 "" {MPLTEXT 1 219 22 "plot(u1f(t), t=0..32);" }
{MPLTEXT 1 219 0 "" }}}{EXCHG {PARA 209 "> " 0 "" {MPLTEXT 1 219 23 "p
lot(u1f(t), t=0..100);" }{MPLTEXT 1 219 0 "" }}}{EXCHG {PARA 209 "> " 
0 "" {MPLTEXT 1 219 37 "MSF2:=subs(\{w=2,w0=4,b=1/4,F=4\},MSF);" }
{MPLTEXT 1 219 0 "" }}}{EXCHG {PARA 209 "> " 0 "" {MPLTEXT 1 219 59 "u
2f:= unapply(rhs(dsolve(\{MSF2,D(u)(0)=1,u(0)=1\},u(t))),t);" }
{MPLTEXT 1 219 0 "" }}}{EXCHG {PARA 209 "> " 0 "" {MPLTEXT 1 219 24 "p
lot(u2f(t), t = 0..32);" }{MPLTEXT 1 219 0 "" }}}{EXCHG {PARA 209 "> "
 0 "" {MPLTEXT 1 219 32 "plot(\{u1f(t), u2f(t)\}, t=0..30);" }
{MPLTEXT 1 219 0 "" }}}{EXCHG {PARA 208 "" 0 "" {TEXT 218 0 "" }}
{PARA 212 "" 0 "" {TEXT 223 56 "Transient and Steady State parts of th
e solution u1f(t):" }{TEXT 223 0 "" }}{PARA 208 "" 0 "" {TEXT 218 0 ""
 }}}{EXCHG {PARA 209 "> " 0 "" {MPLTEXT 1 219 38 "MSF1:=subs(\{w=2,w0=
4,b=1/12,F=4\},MSF);" }{MPLTEXT 1 219 0 "" }}}{EXCHG {PARA 208 "" 0 ""
 {TEXT 218 0 "" }}{PARA 208 "" 0 "" {TEXT 218 17 "General Solution:" }
{TEXT 218 0 "" }}{PARA 208 "" 0 "" {TEXT 218 0 "" }}}{EXCHG {PARA 209 
"> " 0 "" {MPLTEXT 1 219 49 "u1fg:= unapply(rhs(dsolve(MSF1,u(t))),t,_
C1,_C2);" }{MPLTEXT 1 219 0 "" }}}{EXCHG {PARA 208 "" 0 "" {TEXT 218 
0 "" }}{PARA 208 "" 0 "" {TEXT 218 18 "Steady State part:" }{TEXT 218 
0 "" }}{PARA 208 "" 0 "" {TEXT 218 0 "" }}}{EXCHG {PARA 209 "> " 0 "" 
{MPLTEXT 1 219 19 "u1fSS:=u1fg(t,0,0);" }{MPLTEXT 1 219 0 "" }}}
{EXCHG {PARA 209 "> " 0 "" {MPLTEXT 1 219 21 "plot(u1fSS, t=0..20);" }
{MPLTEXT 1 219 0 "" }}}{EXCHG {PARA 208 "" 0 "" {TEXT 218 0 "" }}
{PARA 208 "" 0 "" {TEXT 218 31 "Transient part of the solution:" }
{TEXT 218 0 "" }}{PARA 208 "" 0 "" {TEXT 218 0 "" }}{PARA 208 "" 0 "" 
{TEXT 218 24 "First let's solve an IVP" }{TEXT 218 0 "" }}{PARA 208 ""
 0 "" {TEXT 218 0 "" }}}{EXCHG {PARA 209 "> " 0 "" {MPLTEXT 1 219 61 "
u1f:= unapply(rhs(dsolve(\{MSF1, u(0)=1, D(u)(0)=1\},u(t))),t);" }
{MPLTEXT 1 219 0 "" }}}{EXCHG {PARA 209 "> " 0 "" {MPLTEXT 1 219 19 "u
1ft:=u1f(t)-u1fSS;" }{MPLTEXT 1 219 0 "" }}}{EXCHG {PARA 209 "> " 0 ""
 {MPLTEXT 1 219 20 "plot(u1ft, t=0..20);" }{MPLTEXT 1 219 0 "" }}}
{EXCHG {PARA 209 "> " 0 "" {MPLTEXT 1 219 28 "plot(\{u1fSS,u1ft\}, t=0
..20);" }{MPLTEXT 1 219 0 "" }}}{EXCHG {PARA 208 "" 0 "" {TEXT 218 0 "
" }}{PARA 208 "" 0 "" {TEXT 218 22 "Superposition of both:" }{TEXT 
218 0 "" }}{PARA 208 "" 0 "" {TEXT 218 0 "" }}}{EXCHG {PARA 209 "> " 0
 "" {MPLTEXT 1 219 26 "plot(u1fSS+u1ft, t=0..20);" }{MPLTEXT 1 219 0 "
" }}}{EXCHG {PARA 208 "" 0 "" {TEXT 218 0 "" }}{PARA 208 "" 0 "" 
{TEXT 218 21 "Problem 6 Section 3.9" }{TEXT 218 0 "" }}{PARA 208 "" 0 
"" {TEXT 218 8 "part (d)" }{TEXT 218 0 "" }}{PARA 208 "" 0 "" {TEXT 
218 0 "" }}}{EXCHG {PARA 209 "> " 0 "" {MPLTEXT 1 219 0 "" }}}{EXCHG 
{PARA 209 "> " 0 "" {MPLTEXT 1 219 60 "MSF3:=diff(u(t),t$2) + 10*diff(
u(t),t) + 98*u(t)=2*sin(w*t);" }{MPLTEXT 1 219 0 "" }}}{EXCHG {PARA 
209 "> " 0 "" {MPLTEXT 1 219 50 "u3fg:=unapply(rhs(dsolve(MSF3,u(t))),
t,w,_C1,_C2);" }{MPLTEXT 1 219 0 "" }}}{EXCHG {PARA 209 "> " 0 "" 
{MPLTEXT 1 219 14 "u3fg(t,w,0,0);" }{MPLTEXT 1 219 0 "" }}}{EXCHG 
{PARA 209 "> " 0 "" {MPLTEXT 1 219 80 "Ampl:=w->sqrt((-20*w)^2/(9604-9
6*w^2+w^4)^2 +(2*(-98+w^2)/(9604-96*w^2+w^4))^2);" }{MPLTEXT 1 219 0 "
" }}}{EXCHG {PARA 209 "> " 0 "" {MPLTEXT 1 219 23 "DAmpl:=diff(Ampl(w)
,w);" }{MPLTEXT 1 219 0 "" }}}{EXCHG {PARA 209 "> " 0 "" {MPLTEXT 1 
219 17 "solve(DAmpl=0,w);" }{MPLTEXT 1 219 0 "" }}}{EXCHG {PARA 209 ">
 " 0 "" {MPLTEXT 1 224 0 "" }}}{EXCHG {PARA 209 "> " 0 "" {MPLTEXT 1 
224 0 "" }}}{PARA 213 "" 0 "" {TEXT -1 0 "" }}}{MARK "0 0 0" 0 }
{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }