{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" 0 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 "" 11 12 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }1 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Maple P lot" 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" 0 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 Font 2" -1 257 1 {CSTYLE "" -1 -1 "Courier" 0 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 11 "bounce4.mws" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 320 "A large ball and sm all ball fall together so that after the large ball hits the floor, it impacts the small ball and sends the small ball high into the air. Th is can be demonstrated on a ringstand with masses and springs. The lar ge and small masses are separated by a spring, and there is a spring b elow the large mass. " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 293 "This worksheet models that situation. It has a spring between the large and small mass, and a spring below the large mass, \+ between it and the floor. It illustrates use of Heaviside functions to model contact between bodies with a spring. Motions of the bodies ar e found as a function of time." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }} {PARA 0 "" 0 "" {TEXT -1 118 "The idea is to determine the separation \+ between large and small mass for the largest rebound height of the sma ll mass." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 42 "y1 and y2 released from rest, y1 a bove y2." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 26 "y1 > y2 y1 is above y2. " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }} {PARA 0 "" 0 "" {TEXT -1 28 "k=2000 N/m, m1 = 1, m2 = 2" }}{PARA 0 " " 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "restart;with(plots):" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 63 "Spring compression. Force comes on when compression is po sitive" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "c2:=-y2(t)+L; " } }{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#c2G,&-%#y2G6#%\"tG!\"\"%\"LG\"\"\" " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "c1:=L+y2(t)-y1(t);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%#c1G,(%\"LG\"\"\"-%#y2G6#%\"tGF'-%#y 1GF*!\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 55 "eq1:=+k*c1*Hea viside(c1)-m1*98/10 = m1*diff(y1(t),t,t);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$eq1G/,&*(%\"kG\"\"\",(%\"LGF)-%#y2G6#%\"tGF)-%#y1GF. !\"\"F)-%*HeavisideG6#F*F)F)%#m1G#!#\\\"\"&*&F6F)-%%diffG6$-F<6$F0F/F/ F)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "values:=\{m1=1/5,m2=2 ,k=2000,L=1/2\};" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'valuesG<&/%#m2G \"\"#/%\"kG\"%+?/%\"LG#\"\"\"F(/%#m1G#F/\"\"&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "eq1s:=subs(values,eq1);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%eq1sG/,&*&,(#\"\"\"\"\"#F*-%#y2G6#%\"tGF*-%#y1GF.!\" \"F*-%*HeavisideG6#F(F*\"%+?#!#\\\"#DF*,$-%%diffG6$-F<6$F0F/F/#F*\"\"& " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 75 "eq2:=+k*c2*Heaviside(c2)-k*c1*Heaviside(c1) -m 2*98/10 = m2*diff(y2(t),t,t);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%$eq 2G/,(*(%\"kG\"\"\",&-%#y2G6#%\"tG!\"\"%\"LGF)F)-%*HeavisideG6#F*F)F)*( F(F),(F0F)F+F)-%#y1GF-F/F)-F26#F5F)F/%#m2G#!#\\\"\"&*&F:F)-%%diffG6$-F @6$F+F.F.F)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "eq2s:=subs(v alues,eq2);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%%eq2sG/,(*&,&-%#y2G6# %\"tG!\"\"#\"\"\"\"\"#F/F/-%*HeavisideG6#F(F/\"%+?*&,(F.F/F)F/-%#y1GF+ F-F/-F26#F6F/!%+?#!#)*\"\"&F/,$-%%diffG6$-FA6$F)F,F,F0" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "eqs:=\{eq1s,eq2s\};" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%$eqsG<$/,(*&,&-%#y2G6#%\"tG!\"\"#\"\"\"\"\"#F0F0 -%*HeavisideG6#F)F0\"%+?*&,(F/F0F*F0-%#y1GF,F.F0-F36#F7F0!%+?#!#)*\"\" &F0,$-%%diffG6$-FB6$F*F-F-F1/,&F6F5#!#\\\"#DF0,$-FB6$-FB6$F8F-F-#F0F? 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