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OpenProblemLibrary/FortLewis/DiffEq/2-Higher-order/06-Forcing-resonance Expand file tree Collapse file tree 3 files changed +32
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lines changed Original file line number Diff line number Diff line change @@ -44,6 +44,11 @@ TEXT(beginproblem());
4444
4545Context("Numeric");
4646Context()->variables->are(t=>"Real");
47+ Context()->variables->set(t=>{limits=>[-1,0]});
48+ Context()->flags->set(
49+ reduceConstants => 0,
50+ reduceConstantFunctions => 0,
51+ );
4752
4853$m = 2;
4954$c = 8;
@@ -54,14 +59,14 @@ $w = 8;
5459
5560$F = Formula("2*$a cos($w t)")->reduce();
5661
57- $c1 = Compute ("3*$a/200");
58- $c2 = Compute("(2*$c1-8 *$a/50)/6 ");
59- $c3 = Compute ("-3*$a/200");
60- $c4 = Compute ("$a/50");
62+ $c1 = Formula ("3*$a/200");
63+ $c2 = Formula("-13 *$a/600 ");
64+ $c3 = Formula ("-3*$a/200");
65+ $c4 = Formula ("$a/50");
6166
62- $y = Compute ("$c1 e^(-2t) cos(6t) + $c2 e^(-2t) sin(6t) + $c3 cos(8t) + $c4 sin(8t)");
67+ $y = Formula ("$c1 e^(-2t) cos(6t) + $c2 e^(-2t) sin(6t) + $c3 cos(8t) + $c4 sin(8t)");
6368
64- $yinfinity = Compute ("$c3 cos(8t) + $c4 sin(8t)");
69+ $yinfinity = Formula ("$c3 cos(8t) + $c4 sin(8t)");
6570
6671
6772Context()->texStrings;
Original file line number Diff line number Diff line change @@ -44,6 +44,11 @@ TEXT(beginproblem());
4444
4545Context("Numeric");
4646Context()->variables->are(t=>"Real");
47+ Context()->variables->set(t=>{limits=>[-1,0]});
48+ Context()->flags->set(
49+ reduceConstants => 0,
50+ reduceConstantFunctions => 0,
51+ );
4752
4853$m = 2;
4954$c = 8;
@@ -54,13 +59,14 @@ $w = 8;
5459
5560$F = Formula("$a e^(-t)")->reduce();
5661
57- $c1 = Compute("-$a/74");
58- $c2 = Compute("($a/74 + 2*$c1)/6");
59- $c3 = Compute("$a/74");
62+ $c1 = Formula("-$a/74");
63+ $c2 = Formula("-$a/444");
64+ $c3 = Formula("$a/74");
65+
6066
61- $y = Compute ("$c1 e^(-2t) cos(6t) + $c2 e^(-2t) sin(6t) + $c3 e^(-t)");
67+ $y = Formula ("$c1 e^(-2t) cos(6t) + $c2 e^(-2t) sin(6t) + $c3 e^(-t)");
6268
63- $yinfinity = Compute ("0");
69+ $yinfinity = Formula ("0");
6470
6571
6672Context()->texStrings;
Original file line number Diff line number Diff line change @@ -45,10 +45,10 @@ TEXT(beginproblem());
4545
4646Context("Numeric");
4747Context()->variables->are(t=>"Real");
48- Context()->variables->set(t=>{limits=>[-3,2 ]});
48+ Context()->variables->set(t=>{limits=>[-1,0 ]});
4949Context()->flags->set(
50- tolerance => 0.001 ,
51- tolType => "absolute" ,
50+ reduceConstants => 0,
51+ reduceConstantFunctions => 0 ,
5252);
5353
5454$m = 2;
@@ -60,14 +60,15 @@ $w = 6;
6060
6161$F = Formula("$a sin($w t)")->reduce();
6262
63- $c1 = Compute("6 *$a/296 ");
64- $c2 = Compute("(2*$c1 - 6*$ a/296)/6 ");
65- $c3 = Compute ("-6 *$a/296 ");
66- $c4 = Compute ("$a/296");
63+ $c1 = Formula("3 *$a/148 ");
64+ $c2 = Formula("$ a/296");
65+ $c3 = Formula ("-3 *$a/148 ");
66+ $c4 = Formula ("$a/296");
6767
68- $y = Compute("e^(-2t) ($c1 cos(6t) + $c2 sin(6t)) + $c3 cos(6t) + $c4 sin(6t)");
6968
70- $yinfinity = Compute("$c3 cos(6t) + $c4 sin(6t)");
69+ $y = Formula("e^(-2t) ($c1 cos(6t) + $c2 sin(6t)) + $c3 cos(6t) + $c4 sin(6t)");
70+
71+ $yinfinity = Formula("$c3 cos(6t) + $c4 sin(6t)");
7172
7273
7374Context()->texStrings;
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