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{SECT 0 {EXCHG {PARA 0 "" 0 "" {TEXT 256 13 "Normal modes " }{TEXT 
257 169 "of two masses linearly connected with three springs (Figure 1
1.3.1 in Fowles) - this shows the Symmetric mode (Figure 11.3.5) and t
he Anti-Symmetric mode (Figure 11.3.6)" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 20 "restart:with(plots):" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 88 "m:=1: k:=1: kp :=0.2: x1i :=1: x2i := 1: v1i := 0: v2
i := 0:  # CHANGE THESE VALUES ONLY" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 40 "w1 := sqrt(k/m): w2 := sqrt((k+2*kp)/m):" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "a11 := x1i: a21 := x2i:" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 43 "x11 := a11*cos(w1*t): x21 := a21*co
s(w1*t):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 190 "plot([-3+x11,3
+x21],t=0..15,view=-5..+5,thickness=[2,2],numpoints=1000,discont=true,
color=[red,blue],labels=[\"t\",\"X1\"],title =\"Normal Mode 1(Anti-sym
metric): X1=Red, X2=Blue\",resolution=50);" }}}{EXCHG {PARA 0 "" 0 "" 
{TEXT -1 161 "           Note : we have placed the \"equilibrium point
\" for each mass at 3 units from the origin on either side (this avoid
s the graphs overlapping each other)." }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 68 "a12 := \+
x1i: a22 := -x2i: x12 := a12*cos(w2*t): x22 := a22*cos(w2*t):" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 194 "plot([-3+x12,3+x22],t=0..15
,view=-5.0..+5,thickness=[2,2],numpoints=1000,discont=true,color=[red,
blue],labels=[\"t\",\"X1\"],title =\"Normal Mode 2 (Anti-symmetric) : \+
X1=Red, X2=Blue\",resolution=50);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 
71 "Note .. the second graph has the masses oscillating opposite each \+
other" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "13" 0 
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