{VERSION 2 3 "IBM INTEL NT" "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 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 "Times" 1 12 0 0 0 1 2 2 2 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 } {PSTYLE "R3 Font 0" -1 256 1 {CSTYLE "" -1 -1 "Helvetica" 1 12 255 0 0 1 2 1 2 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "R3 Fo nt 2" -1 257 1 {CSTYLE "" -1 -1 "Courier" 1 12 0 0 0 1 2 2 2 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }} {SECT 0 {EXCHG {PARA 0 "" 0 "" {TEXT -1 10 "contact.ms" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 274 "A program to illust rate use of Heaviside functions to model contact between bodies with a spring. The spring is attached to the first body, which is moving. Th e first body strikes the second body, which is at rest. Motions of the bodies are then found as a function of time." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 92 "x1 refers to the body whi ch is moving initially. x2 refers to the initially stationary body" } }{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "re start;with(plots):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 40 "d:=-x 2(t)+x1(t)+x0; # spring compression" }}{PARA 11 "" 1 "" {XPPMATH 20 "6 #>%\"dG,(-%#x2G6#%\"tG!\"\"-%#x1GF(\"\"\"%#x0GF-" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 44 "eq1:=-k*d*Heaviside(d) = m1*diff(x1(t),t,t); " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$eq1G/,$*(%\"kG\"\"\",(-%#x2G6#% \"tG!\"\"-%#x1GF-F)%#x0GF)F)-%*HeavisideG6#F*F)F/*&%#m1GF)-%%diffG6$-F 96$F0F.F.F)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 46 "eq2:=+k*(d)* Heaviside(d) = m2*diff(x2(t),t,t);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6# >%$eq2G/*(%\"kG\"\"\",(-%#x2G6#%\"tG!\"\"-%#x1GF,F(%#x0GF(F(-%*Heavisi deG6#F)F(*&%#m2GF(-%%diffG6$-F86$F*F-F-F(" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 32 "values:=\{m1=1,m2=1,k=10,x0=1/2\};" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'valuesG<&/%#m1G\"\"\"/%#m2GF(/%\"kG\"#5/%#x0G#F (\"\"#" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 39 "eqs:=subs(values, eq1),subs(values,eq2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$eqsG6$/,$ *&,(-%#x2G6#%\"tG!\"\"-%#x1GF,\"\"\"#F1\"\"#F1F1-%*HeavisideG6#F)F1!#5 -%%diffG6$-F96$F/F-F-/,$F(\"#5-F96$-F96$F*F-F-" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 77 "s:=dsolve(\{eqs,x1(0)=0,D(x1)(0)=5,x2(0)=1,D(x 2)(0)=0\},\{x1(t),x2(t)\},numeric);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6 #>%\"sG:6#%(rkf45_xG6'%\"iG%(rkf45_sG%)outpointG%#r1G%#r2G6#%aoCopyrig ht~(c)~1993~by~the~University~of~Waterloo.~All~rights~reserved.G6\"C&> 8&-%&evalfG6#9$@$52-%$absG6#,$F3!\"\"-F<6#,&&%,loc_controlG6#\"\"#\"\" \"F3F?4-%'memberG6$&FD6#\"\"'<*$FG\"\"!$FFFQ$F?FQ$!\"#FQF?FGFUFFC%>FD- %%copyG6#=F06#;FG\"#ZE\\[lP\"#CFQ\"\"*\"%+5\"#SFQ\"#DFQ\"#5FQ\"#TFQ\"# EFQ\"#6FQ\"#UFQ\"#FFQ\"#7FQ\"#VFQ\"#GFQ\"#8FQ\"#WFQ\"#HFQ\"#9FQ\"#XFQ 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