{VERSION 3 0 "SUN SPARC SOLARIS" "3.0" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 1 0 0 0 0 }{CSTYLE "2D Math" -1 2 "Times" 0 1 0 0 0 0 0 0 2 0 0 0 0 0 0 }{CSTYLE "2D Output" 2 20 "" 0 1 0 0 255 1 0 0 0 0 0 0 0 0 0 } {PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Maple Output" 0 11 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }3 3 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Maple Plot" 0 13 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }3 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }} {SECT 0 {EXCHG {PARA 0 "" 0 "" {TEXT -1 11 "p. 245 5-8" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 101 "g:=32; m:=5; k:=5/(1/2)/g; x0:=1/1 0; v0:=-1/10; i5:=\{m*diff(x(t),t,t)+k*x(t)=0, x(0)=x0, D(x)(0)=v0\}; " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "s5:=rhs(dsolve(i5,x(t)) );" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "plot(s5,t=0..6);" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "fsolve(diff(s5,t),t=3.5..4.5 );" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "evalf(subs(t=%,s5)); " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 87 "m:=5; k:=5/2/g; x0:=-1; v0:=-1/3; i5:=\{m*diff(x(t),t,t)+k*x(t)=0, x(0)=x0, D(x)(0)=v0\};" }} }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "s5:=rhs(dsolve(i5,x(t)));" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "plot(s5,t=0..6);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "fsolve(diff(s5,t),t=0..1);" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 91 "m:=1/2; k:=m/2/g; x0:=1/2; v 0:=-1/2; i5:=\{m*diff(x(t),t,t)+k*x(t)=0, x(0)=x0, D(x)(0)=v0\}; " }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "s5:=rhs(dsolve(i5,x(t)));" } }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "plot(s5,t=0..6);" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "fsolve(s5,t=.8..1);" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 73 "#8. The chief difficulty is conve rting pounds to slugs! If g=32 ft/s^2:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 58 "restart:p1:=2*Pi/sqrt(k/m)=3; p2:=2*Pi/sqrt(k/(m+2/32 ))=4;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "solve(\{p1,p2\},\{ m,k\});" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 28 "p. 253. These are all easy." }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 54 "Coupled things: first \+ masses and springs. p. 266, 1." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 118 "m1:=1; m2:=2; k1:=4; k2:=10/3; d11:=diff(x(t),t,t)*m1=-k1*(x( t)-y(t)); \nd12:=diff(y(t),t,t)*m2=k1*(x(t)-y(t))-k2*y(t);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 42 "i1:=x(0)=-1, y(0)=0, D(x)(0)=0, D(y )(0)=0;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "s1:=dsolve(\{d11 ,d12,i1\},\{x(t),y(t)\});" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 39 "plot(\{rhs(s1[1]), rhs(s1[2])\}, t=0..1);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "d11d:=diff(d11,t,t);" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 13 "di2o2:=d12/2;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "almost1:=subs(di2o2,d11d);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "solve(d11,y(t));" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "subs(y(t)=%,almost1);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "solve(r^4-22/3*r^2-20/3,r);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "evalf(%);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 115 "m1:=1; m2:=1; k1:=3; k2:=2; d11:=diff(x(t),t,t)*m1=-k1*(x(t)- y(t)); \nd12:=diff(y(t),t,t)*m2=k1*(x(t)-y(t))-k2*y(t);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 42 "i1:=x(0)=-1, y(0)=0, D(x)(0)=0, D(y )(0)=0;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 53 "s1:=dsolve(\{d11 ,d12,i1\},\{x(t),y(t)\}, method=laplace);" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 14 "s1:=evalf(s1);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 40 "plot(\{rhs(s1[1]), rhs(s1[2])\}, t=0..10);" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 20 "d11d:=diff(d11,t,t);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "di2o2:=d12;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "almost1:=subs(di2o2,d11d);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "solve(d11,y(t));" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "subs(y(t)=%,almost1);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "solve(r^4+8*r^2+6,r);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "evalf(%);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 139 "m1:=1; m2:=2; k1:=4; k2:=10/3; b:=1; d11:=diff(x(t),t,t)*m1=-k1*x (t)+k2*(y(t)-x(t)); \nd12:=diff(y(t),t,t)*m2=k2*(x(t)-y(t))-b*diff(y(t ),t);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 42 "i1:=x(0)=-1, y(0)= 0, D(x)(0)=0, D(y)(0)=0;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 53 "s1:=dsolve(\{d11,d12,i1\},\{x(t),y(t)\}, method=laplace);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "si:=evalf(s1);" }}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 1397 "\{x(t) = -.1091856861*exp(-.2219189835*t)* cos(.8763327832*t)+.4016164384e-1*exp(-.2219189835*t)*sin(.8763327832* t)-1.*I*(-.2008082192e-1*exp(-.2219189835*t)*cos(.8763327832*t)-.54592 84307e-1*exp(-.2219189835*t)*sin(.8763327832*t))-1.*I*(.2008082192e-1* exp(-.2219189835*t)*cos(.8763327832*t)+.5459284307e-1*exp(-.2219189835 *t)*sin(.8763327832*t))-.8908143139*exp(-.2808101647e-1*t)*cos(2.85605 9774*t)-.2956531716e-1*exp(-.2808101647e-1*t)*sin(2.856059774*t)-1.*I* (.1478265858e-1*exp(-.2808101647e-1*t)*cos(2.856059774*t)-.4454071569* exp(-.2808101647e-1*t)*sin(2.856059774*t))-1.*I*(-.1478265858e-1*exp(- .2808101647e-1*t)*cos(2.856059774*t)+.4454071569*exp(-.2808101647e-1*t )*sin(2.856059774*t)), y(t) = -.2213528783*exp(-.2219189835*t)*cos(.87 63327832*t)+.6695590658e-1*exp(-.2219189835*t)*sin(.8763327832*t)-10.* I*(-.3347795329e-2*exp(-.2219189835*t)*cos(.8763327832*t)-.1106764391e -1*exp(-.2219189835*t)*sin(.8763327832*t))-10.*I*(.3347795329e-2*exp(- .2219189835*t)*cos(.8763327832*t)+.1106764391e-1*exp(-.2219189835*t)*s in(.8763327832*t))+.2213528783*exp(-.2808101647e-1*t)*cos(2.856059774* t)-.3556726957e-1*exp(-.2808101647e-1*t)*sin(2.856059774*t)-10.*I*(.17 78363479e-2*exp(-.2808101647e-1*t)*cos(2.856059774*t)+.1106764391e-1*e xp(-.2808101647e-1*t)*sin(2.856059774*t))-10.*I*(-.1778363479e-2*exp(- .2808101647e-1*t)*cos(2.856059774*t)-.1106764391e-1*exp(-.2808101647e- 1*t)*sin(2.856059774*t))\};" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "subs(I=0,%);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 38 "plot(\{ rhs(%[1]), rhs(%[2])\}, t=0..50);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "d11d:=diff(d11,t,t);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%d11dG/-%%diffG6$-%\"xG6#%\"tG-%\"$G6$F,\"\"%,&-F'6$F)-F.6$F,\"\" ##!#A\"\"$-F'6$-%\"yGF+F4#\"#5F9" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "di2o2:=d12/2;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%&d i2o2G/-%%diffG6$-%\"yG6#%\"tG-%\"$G6$F,\"\"#,(-%\"xGF+#\"\"&\"\"$F)#! 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