{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 Comment" 2 18 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 } {CSTYLE "" -1 256 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 257 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 258 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 259 "" 1 14 0 0 0 0 0 1 0 0 0 0 0 0 0 } {CSTYLE "" -1 260 "" 1 14 0 0 0 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 261 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 262 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 263 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 264 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 265 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 266 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 267 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 268 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 269 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 270 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 271 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 272 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 273 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 275 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 276 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 277 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 278 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 279 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 280 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 281 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 282 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 283 "" 0 1 0 0 0 0 1 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 "B ullet Item" 0 15 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 } 0 0 0 -1 3 3 0 0 0 0 0 0 15 2 }{PSTYLE "Title" 0 18 1 {CSTYLE "" -1 -1 "" 1 18 0 0 0 0 0 1 1 0 0 0 0 0 0 }3 0 0 -1 12 12 0 0 0 0 0 0 19 0 }{PSTYLE "Part Number" 0 256 1 {CSTYLE "" -1 -1 "Times" 1 12 128 0 0 1 0 1 0 0 0 0 0 0 0 }0 0 0 -1 -1 -1 3 6 0 0 0 0 -1 3 }{PSTYLE "Done" 0 257 1 {CSTYLE "" -1 -1 "Times" 1 12 128 0 0 1 0 1 0 0 0 0 0 0 0 }1 0 0 -1 -1 -1 3 20 0 0 0 0 -1 0 }{PSTYLE "" 0 258 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 "" 0 259 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 18 "" 0 "" {TEXT -1 27 "Entering and Analyzing Da ta" }}{PARA 258 "" 0 "" {TEXT -1 19 "Original Version: " }{TEXT 256 11 "Marie Baehr" }{TEXT -1 10 " 6/22/97" }}{PARA 259 "" 0 "" {TEXT -1 19 "Revised Version : " }{TEXT 257 15 "Earl C. Swallow" }{TEXT -1 10 " 10/11/99" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 79 "This worksheet provides a n example of entering experimental data and using the " }{TEXT 258 5 " stats" }{TEXT -1 23 " package to analyze it." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 259 8 "Problem:" }{TEXT -1 2 " " }}{PARA 0 "" 0 "" {TEXT -1 254 "You have c ollected data in the classroom (see Wordperfect document for further d iscussion) on the position of a freely falling object as a function of time. You know that the relationship between the total distance fall en and the fall time is given by: " }{XPPEDIT 18 0 "Delta x = v0*t+g*t ^2/2" "/*&%&DeltaG\"\"\"%\"xGF%,&*&%#v0GF%%\"tGF%F%*(%\"gGF%*$F*\"\"#F %F.!\"\"F%" }{TEXT -1 11 " (and that " }{XPPEDIT 18 0 "v = v0 + g*t" " /%\"vG,&%#v0G\"\"\"*&%\"gGF&%\"tGF&F&" }{TEXT -1 51 " ). You would li ke to obtain numerical values for " }{TEXT 261 1 "g" }{TEXT -1 5 " and " }{TEXT 262 2 "v0" }{TEXT -1 15 " from the data." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 260 15 "Solution Steps:" }} {PARA 15 "" 0 "" {TEXT -1 29 "Enter the data in array form " }}{PARA 15 "" 0 "" {TEXT -1 13 "Plot the data" }}{PARA 15 "" 0 "" {TEXT -1 26 "Fit the data as distance (" }{TEXT 278 1 "x" }{TEXT -1 25 ") as a fun ction of time (" }{TEXT 279 1 "t" }{TEXT -1 43 ") to get the best quad ratic representation." }}{PARA 15 "" 0 "" {TEXT -1 45 "Equate the coef ficient in the linear term to " }{TEXT 280 3 "v0," }{TEXT -1 41 " and \+ equate the quadratic coefficient to " }{TEXT 281 3 "g/2" }{TEXT -1 1 " ." }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 8 "restart;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "with(linalg);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 58 "In the first approach, you enter the times into one list (" }{TEXT 263 5 "time1" } {TEXT -1 39 ") and the distances into another list (" }{TEXT 264 5 "di st1" }{TEXT -1 61 "). These are then combined to make a list of order ed pairs (" }{TEXT 265 5 "data0" }{TEXT -1 2 ")." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "time1:=[0,.2,.4,.6,.8,1.0];" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "dist1:=[0,.21,.79,1.83,3.15,5.05];" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "pair:=(x,y)->[x,y];" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "data0:=zip(pair,time1,dist1) ;" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 94 "The second (alternative) app roach is to enter the data directly into a list of ordered pairs (" } {TEXT 266 5 "data1" }{TEXT -1 2 ")." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 64 "data1:=[[0,0],[.2,.21],[.4,.79],[.6,1.83],[.8,3.15],[ 1.0,5.05]];" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 10 "Note that " } {TEXT 267 5 "data0" }{TEXT -1 5 " and " }{TEXT 268 5 "data1" }{TEXT -1 68 " are identical. If you only want to plot the data, enter it as for " }{TEXT 269 6 "data 1" }{TEXT -1 35 ". If however, you want to \+ use the " }{TEXT 270 5 "stats" }{TEXT -1 83 " package to analyze it, y ou are probably better off entering it as separate lists (" }{TEXT 271 5 "time1" }{TEXT -1 5 " and " }{TEXT 272 5 "dist1" }{TEXT -1 41 ") . Otherwise, you end up having to pull " }{TEXT 273 5 "data1" }{TEXT -1 7 " apart." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 48 "Now plot the data to see if it looks reasonable." }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 38 "plot(data1,style=point,symbo l=circle);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "with(stats); " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 61 "bestfit:=fit [leastsqua re[[t,x], x=a*t^2+b*t]]([time1,dist]);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 50 "Now suppose you want to c heck this fit. Define a " }{TEXT 275 5 "label" }{TEXT -1 26 " for the right hand side (" }{TEXT 277 3 "rhs" }{TEXT -1 5 ") of " }{TEXT 276 7 "bestfit" }{TEXT -1 37 " and graph it for the values desired." }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "tryme:=rhs(bestfit);" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "with(plots):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 41 "plot1:=plot(tryme,t=0..1.5, color=g reen):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 58 "plot2:=plot(data0 , style=point, symbol=circle, color=red):" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 21 "display(plot1,plot2);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 38 "So now you figure out what we get for " }{TEXT 282 2 "v0 " }{TEXT -1 5 " and " }{TEXT 283 1 "g" }{TEXT -1 1 "." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "0 0 0" 0 } {VIEWOPTS 1 1 0 1 1 1803 }