User:5849206328x: Difference between revisions

Revision as of 15:25, 18 July 2015

$[asy] import slopefield; real e = 2.718281828459045235360287471352662497757247093699959574966967627724076630353; real pi = 3.141592653589793238462643383279502884197169399375105820974944592307816406286; // Label f; // f.p=fontsize(6); xaxis(0,1); yaxis(0,0.5); //real f(real x) { return (-2) * cos(x); } pair g(real t, real k) { return (1/k * 3/5 * (1 - e^(-k * t)), -t/k + 1/k * (4/5 + 1/k) * (1 - e^(-k * t))); } pair g1(real t) { return g(t,1); } pair g2(real t) { return g(t,0.2); } pair h(real t) { return (3/5 * t, -1/2 * t^2 + 4/5 * t); } draw(graph(g1,0,2)); draw(graph(g2,0,2)); draw(graph(h,0,2)); label("$k = 1$",(0.44,0),NE); label("$k = 0.1$",(0.79,0),NE); label("$k = 0$",(0.96,0),NE); //draw(graph(f,-4,4)); limits((0,0),(2,2),Crop); [/asy]$

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User:5849206328x: Difference between revisions

Revision as of 15:25, 18 July 2015

@@ Line 7: / Line 7: @@
 // Label f;
 // f.p=fontsize(6);
-//xaxis(-4,4);
+xaxis(0,1);
-//yaxis(-4,4);
+yaxis(0,0.5);
-//real f1(real x) { return (-2) * cos(x); }
+//real f(real x) { return (-2) * cos(x); }
+pair g(real t, real k) { return (1/k * 3/5 * (1 - e^(-k * t)), -t/k + 1/k * (4/5 + 1/k) * (1 - e^(-k * t))); }
+pair g1(real t) { return g(t,1); }
+pair g2(real t) { return g(t,0.2); }
+pair h(real t) { return (3/5 * t, -1/2 * t^2 + 4/5 * t); }
-//draw(graph(f1,-4,4));
+draw(graph(g1,0,2));
+draw(graph(g2,0,2));
+draw(graph(h,0,2));
-fill((0,0)--(5/8,0)--(5,21/8)--(5,3)--cycle,lightgray);
+label("$k = 1$",(0.44,0),NE);
-draw((0,0)--(5,3));
+label("$k = 0.1$",(0.79,0),NE);
-draw((2,6/5)--(3/2,61/30)--(5/2,79/30)--(3,9/5));
+label("$k = 0$",(0.96,0),NE);
-draw((49/20,19/12)--(69/20,131/60),dashed,EndArrow);
+//draw(graph(f,-4,4));
-draw((5/2,3/2)--(3/2,19/6),dashed,EndArrow);
-draw((9/4,23/12)--(9/4,-7/20),dashed,EndArrow);
-label("$m\mathbf{g}$",(9/4,1/2),E);
+limits((0,0),(2,2),Crop);
-label("$\mathbf{N}$",(3/2,19/6),W);
-label("$\mathbf{f}$",(69/20,131/60),N);
-//limits((-4,-4),(4,4),Crop);
 </asy>