activate

activate

activate

speed up

speed up, then slow down

slow down

y

A

B

C

enable

enablec = false
ymin = -5
ymax = 5
dy = 1
y0options = Sequence((0, i), i, (ceil(ymin / dy) * dy) + dy, ymax - dy, dy)
y0cpoint = Point(y0options)
enableb = false
y0bpoint = Point(y0options)
enablea = true
y0apoint = Point(y0options)
y0c = If(enablec, y(y0cpoint))
dt = 1
y0b = If(enableb, y(y0bpoint))
s1coptions: {(dt, y0c + dy), (dt, y0c - dy)}
y0a = If(enablea, y(y0apoint))
s1boptions: {(dt, y0b + dy), (dt, y0b - dy)}
tmax = 9
tmin: ((-0.1) * tmax)
speeda = 3
s1aoptions: {(dt, y0a + dy), (dt, y0a - dy)}
s1apoint = Point(s1aoptions)
s1aval: y(s1apoint) - y0a
s1acurve = Function(((ℯ^((x * log(2))) - 1) * s1aval) + y0a, 0, tmax)
s23options = Sequence(((floor((0.98 * tmax / dt)) * dt), i), i, (ceil(ymin / dy) * dy) + dy, ymax - dy, dy)
s23apoint = Point(s23options)
s23aval: y(s23apoint)
s3acurve = Function(((y0a - s23aval) * ℯ^((-x))) + s23aval, 0, tmax)
ylabeldisplay: "" + (LaTeX[ylabel]) + ""
grid = Sequence(Segment[(0, i), (tmax, i)], i, (ceil(ymin / dy) * dy) + dy, ymax - dy, dy)
speedb = 1
speedc = 2
pointsul: ((0.7 * tmin) + (0.3 * tmax), (0.8 * ymax) + (0.2 * ymin))
pointsdt: (0.06 * (tmax - tmin))
pointsdy: (0.1 * (ymax - ymin))
S1a: pointsul
S2a: pointsul - (0, pointsdy)
S3a: pointsul - (0, (2 * pointsdy))
S1b: pointsul + (pointsdt, 0)
S2b: pointsul + (pointsdt, (-pointsdy))
S3b: pointsul + (pointsdt, ((-2) * pointsdy))
S1c: pointsul + ((2 * pointsdt), 0)
S2c: pointsul + ((2 * pointsdt), (-pointsdy))
S3c: pointsul + ((2 * pointsdt), ((-2) * pointsdy))
A: pointsul + (0, pointsdy)
B: pointsul + (pointsdt, pointsdy)
C: pointsul + ((2 * pointsdt), pointsdy)
s23bpoint = Point(s23options)
s23cpoint = Point(s23options)
yinfa = If(enablea, If[speeda ≟ 1, If[s1aval ≟ 1, ymax, ymin], s23aval])
s1bpoint = Point(s1boptions)
s1bval: y(s1bpoint) - y0b
s1cpoint = Point(s1coptions)
s1cval: y(s1cpoint) - y0c
s23bval: y(s23bpoint)
s23cval: y(s23cpoint)
yinfb = If(enableb, If[speedb ≟ 1, If[s1bval ≟ 1, ymax, ymin], s23bval])
flogistic(x) = (1 / (1 + ℯ^((-4 * (x - dt)))) - 1 / (1 + ℯ^((4 * dt)))) / (1 - 1 / (1 + ℯ^((4 * dt))))
s2acurve = Function(((s23aval - y0a) * flogistic(x)) + y0a, 0, tmax)
fexp(x) = ℯ^((x * log(2))) - 1
s1bcurve = Function((fexp(x) * s1bval) + y0b, 0, tmax)
s1ccurve = Function((fexp(x) * s1cval) + y0c, 0, tmax)
s2bcurve = Function(((s23bval - y0b) * flogistic(x)) + y0b, 0, tmax)
s2ccurve = Function(((s23cval - y0c) * flogistic(x)) + y0c, 0, tmax)
s3bcurve = Function(((y0b - s23bval) * ℯ^((-x))) + s23bval, 0, tmax)
s3ccurve = Function(((y0c - s23cval) * ℯ^((-x))) + s23cval, 0, tmax)
yinfc = If(enablec, If[speedc ≟ 1, If[s1cval ≟ 1, ymax, ymin], s23cval])
speedprofilea = If(enablea, If[yinfa ≟ y0a, 3, speeda])
speedprofileb = If(enableb, If[yinfb ≟ y0b, 3, speedb])
speedprofilec = If(enablec, If[yinfb ≟ y0c, 3, speedc])