{VERSION 2 3 "SUN SPARC SOLARIS" "2.3" } {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 Comment" 2 18 "" 0 1 0 0 0 0 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 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 29 "4.10 p. 214 # 1, 4, 27, 32" }}{PARA 0 "" 0 "" {TEXT -1 18 "5.1 p. 245 # 8" }}{PARA 0 "" 0 "" {TEXT -1 22 "5.2 p. 253 # 5, 10" }}{PARA 0 "" 0 "" {TEXT -1 18 "5.3 p. 259 # 3" }}{PARA 0 "" 0 "" {TEXT -1 54 "p. 214 #3 Conv ert IVP to a system IVP in normal form." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 106 "i3:=\{diff(y(x),x,x,x,x)-diff(y(x),x,x,x)+7*y(x)=cos (x), y(0)=1, D(y)(0)=1, D(D(y))(0)=0, D(D(D(y)))(0)=2\};" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "factor(l^4-l^3+7);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "dsolve(i3,y(x));" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 4 "Let " }{XPPEDIT 18 0 "y[1]=y" "/&%\"yG6#\"\"\"F$ " }{TEXT -1 7 ", etc.:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 155 " s3:=\{diff(y1(t),t)=y2(t), y1(0)=1,\n diff(y2(t),t)=y3(t), y2(0)=1 ,\n diff(y3(t),t)=y4(t), y3(0)=0,\n diff(y4(t),t)=y4(t)-7*y1(t )+cos(t), y4(0)=2\};" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "dso lve(s3,\{y1(t),y2(t),y3(t),y4(t)\});" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 36 "p. 214 #5 Use elimination to solve:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 66 "s5:=\{diff(x(t),t)+diff(y(t),t)=-2*y(t), x(t)-2*y( t)=diff(y(t),t)\};" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "dsolv e(s5,\{x(t),y(t)\});" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 58 "p. 214 #2 9 A mixing problem. See whiteboard or the book." }}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 86 "s29:=\{diff(x(t),t)=15-x(t)/10, x(0)=50,\n \+ diff(y(t),t)=x(t)/10-y(t)/10, y(0)=100\};" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "dsolve(s29,\{x(t),y(t)\});" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 118 "plot(\{-10*t*exp(-1/10*t)-50*exp(-1/10*t)+15 0,50*exp(-1/10*t)+exp(-1/10*t)*(150*exp(1/10*t)-150)\},t=0..80,color=b lack);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 94 "s29:=\{diff(x(t), t)=12-x(t)/10+y(t)/50, x(0)=50,\n diff(y(t),t)=x(t)/10-y(t)/10, y (0)=100\};" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "dsolve(s29,\{x(t),y(t)\});" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 611 "plot(\{25*exp(1/50*(-5+5^(1 /2))*t)+25*exp(-1/50*(5+5^(1/2))*t)-10*5^(1/2)*exp(-1/50*(5+5^(1/2))*t )+10*5^(1/2)*exp(1/50*(-5+5^(1/2))*t)+(-3000+1500*exp(1/50*(-5+5^(1/2) )*t)+1500*exp(-1/50*(5+5^(1/2))*t)-300*5^(1/2)*exp(-1/50*(5+5^(1/2))*t )+300*5^(1/2)*exp(1/50*(-5+5^(1/2))*t))/(-5+5^(1/2))/(5+5^(1/2)),-25*5 ^(1/2)*exp(-1/50*(5+5^(1/2))*t)+25*5^(1/2)*exp(1/50*(-5+5^(1/2))*t)+50 *exp(1/50*(-5+5^(1/2))*t)+50*exp(-1/50*(5+5^(1/2))*t)+(-3000-1500*5^(1 /2)*exp(-1/50*(5+5^(1/2))*t)+1500*5^(1/2)*exp(1/50*(-5+5^(1/2))*t)+150 0*exp(1/50*(-5+5^(1/2))*t)+1500*exp(-1/50*(5+5^(1/2))*t))/(-5+5^(1/2)) /(5+5^(1/2))\}, t=0..100);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 149 "p. 214 #32 Just a comment: this is a good problem, and could be turned into a project.\n---------------------------------------------------- --------" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 9 "p. 245 #6" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 159 "restart:g:=981/100; m:=5; s:=2; k: =m*g/s; # spring constant\ni6:=\{m*diff(x(t),t,t)+k*x(t)=0,x(0)=-1,D(x )(0)=-1/3\};\ns6:=dsolve(i6,x(t));\nplot(rhs(s6),t=0..6.28);" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 62 "fsolve(diff(rhs(s6),t)=0,t,1 .0..2.0); # find the first maximum" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "evalf(subs(t=\",rhs(s6)));" }}}{EXCHG {PARA 0 "" 0 " " {TEXT -1 9 "p. 253 #7" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 168 "m:=2; s:=49/100; b:=8*sqrt(5); k:=m*g/s; # the 49 is cm\ni7:=\{x(0)=1 0/100,D(x)(0)=2,m*diff(x(t),t,t)+b*diff(x(t),t)+k*x(t)=0\};\ns7:=dsolv e(i7,x(t));\nplot(rhs(s7),t=0..1);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 63 "solve(diff(rhs(s7),t)=0,t); evalf(\"); evalf(subs(t= \",rhs(s7)));" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 9 "p. 259 #2" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 168 "g:=32; m:=8/g; k:=10; b:=1; f:=t->2*cos(2*t);\ni2:=\{x(0)=0,D(x)(0)=0,m*diff(x(t),t,t)+b*diff(x(t ),t)+k*x(t) =f(t)\};\ndsolve(i2,x(t)); scos2:=rhs(dsolve(i2,x(t),lapla ce));" }{TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 118 "The lap lace option results in more compact output because of the way Maple \+ dsolve solves inhomogeneous equations." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 49 "res_freq:=sqrt(k/m-b^2/(2*m^2))/(2*Pi); evalf(\");" } }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "p1:=plot(scos2,t=0..8):" } }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 63 "Change the frequency to the reso nance [sic] frequency. Need " }{XPPEDIT 18 0 "2pi" "*&\"\"#\"\"\"%# piGF$" }{TEXT -1 44 " multipler to convert to angular frequency." }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 156 "g:=32; m:=8/g; k:=10; b:=1; f:=t->2*cos(28*t/10);\ni2:=\{x(0)=0,D(x)(0)=0,m*diff(x(t),t,t)+b*diff (x(t),t)+k*x(t) =f(t)\};\nscos9t:=rhs(dsolve(i2,x(t),laplace));" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "p2:=plot(scos9t,t=0..8):" }} }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "plots[display](\{p1,p2\}); " }}{PARA 13 "" 1 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 90 "Look up display in the plots package: it is going to be very us eful in the near future." }}}}{MARK "35 0 0" 90 }{VIEWOPTS 1 1 0 1 1 1803 }