June 2018 Update

Task/Animate-a-pendulum/BASIC/animate-a-pendulum-1.basic

@@ -0,0 +1,29 @@
+      MODE 8
+      *FLOAT 64
+      VDU 23,23,4;0;0;0; : REM Set line thickness
+
+      theta = RAD(40) : REM initial displacement
+      g = 9.81 : REM acceleration due to gravity
+      l = 0.50 : REM length of pendulum in metres
+
+      REPEAT
+        PROCpendulum(theta, l)
+        WAIT 1
+        PROCpendulum(theta, l)
+        accel = - g * SIN(theta) / l / 100
+        speed += accel / 100
+        theta += speed
+      UNTIL FALSE
+      END
+
+      DEF PROCpendulum(a, l)
+      LOCAL pivotX, pivotY, bobX, bobY
+      pivotX = 640
+      pivotY = 800
+      bobX = pivotX + l * 1000 * SIN(a)
+      bobY = pivotY - l * 1000 * COS(a)
+      GCOL 3,6
+      LINE pivotX, pivotY, bobX, bobY
+      GCOL 3,11
+      CIRCLE FILL bobX + 24 * SIN(a), bobY - 24 * COS(a), 24
+      ENDPROC

Task/Animate-a-pendulum/BASIC/animate-a-pendulum-2.basic

@@ -0,0 +1,24 @@
+10 GOSUB 1000
+20 THETA = π/2
+30 G = 9.81
+40 L = 0.5
+50 SPEED = 0
+60 PX = 20
+70 PY = 1
+80 BX = PX+L*20*SIN(THETA)
+90 BY = PY-L*20*COS(THETA)
+100 PRINT CHR$(147);
+110 FOR X=PX TO BX STEP (BX-PX)/10
+120 Y=PY+(X-PX)*(BY-PY)/(BX-PX)
+130 PRINT CHR$(19);LEFT$(X$,X);LEFT$(Y$,Y);"."
+140 NEXT
+150 PRINT CHR$(19);LEFT$(X$,BX);LEFT$(Y$,BY);CHR$(113)
+160 ACCEL=G*SIN(THETA)/L/50
+170 SPEED=SPEED+ACCEL/10
+180 THETA=THETA+SPEED
+190 GOTO 80
+980 REM ** SETUP STRINGS TO BE USED **
+990 REM ** FOR CURSOR POSITIONING   **
+1000 FOR I=0 TO 39: X$ = X$+CHR$(29): NEXT
+1010 FOR I=0 TO 24: Y$ = Y$+CHR$(17): NEXT
+1020 RETURN

Task/Animate-a-pendulum/BASIC/animate-a-pendulum-3.basic

@@ -0,0 +1,22 @@
+Const PI = 3.141592920
+Dim As Double theta, g, l, accel, speed, px, py, bx, by
+theta = PI/2
+g = 9.81
+l = 1
+speed = 0
+px = 320
+py = 10
+Screen 17 '640x400 graphic
+Do
+    bx=px+l*300*Sin(theta)
+    by=py-l*300*Cos(theta)
+    Cls
+    Line (px,py)-(bx,by)
+    Circle (bx,by),5,,,,,F
+    accel=g*Sin(theta)/l/100
+    speed=speed+accel/100
+    theta=theta+speed
+    Draw String (0,370), "Pendulum"
+    Draw String (0,385), "Press any key to quit"
+    Sleep 10
+Loop Until Inkey()<>""

Task/Animate-a-pendulum/JavaScript/animate-a-pendulum-2.js

@@ -17,9 +17,9 @@
 			in_angle.value = 0;
 			var cx = 150, cy = 50;
 			var radius = 100; // cm
-			var g = 981; // cm/s^2
+			var g = 9.81; // m/s^2
 			var angle = 0; // radians
-			var vel = 0; // cm/s
+			var vel = 0; // m/s
 			var dx = 0.02; // s
 			var acc, vel, penx, peny;
 			var timerFunction = null;
@@ -33,9 +33,9 @@
 				if(!timerFunction) timerFunction = setInterval(swing, dx * 1000);
 			}
 			function swing(){
-				acc = g * Math.cos(angle) * dx;
-				vel += acc * dx;
-				angle += vel * dx;
+				acc = g * Math.cos(angle);
+				vel += acc * dx;//Convert m/s/s to m/s
+				angle += vel/(radius/100) * dx; //convert m/s into rad/s and then into rad
 				setPenPos();
 			}
 			function setPenPos(){

Task/Animate-a-pendulum/Julia/animate-a-pendulum.julia

@@ -0,0 +1,46 @@
+using Luxor
+using Colors
+using BoundaryValueDiffEq
+
+# constants for differential equations and movie
+const g = 9.81
+const L = 1.0                         # pendulum length in meters
+const bobd = 0.10                     # pendulum bob diameter in meters
+const framerate = 50.0                # intended frame rate/sec
+const t0 = 0.0                        # start time (s)
+const tf = 2.3                        # end simulation time (s)
+const dtframe = 1.0/framerate         # time increment per frame
+const tspan = linspace(t0, tf, Int(floor(tf*framerate)))  # array of time points in animation
+
+const bgcolor = "black"               # gif background
+const leaderhue = (0.80, 0.70, 0.20)  # gif swing arm hue light gold
+const hslcolors = [HSL(col) for col in (distinguishable_colors(
+                   Int(floor(tf*framerate)+3),[RGB(1,1,1)])[2:end])]
+const giffilename = "pendulum.gif"    # output file
+
+# differential equations
+simplependulum(t,u,du) = (θ=u[1]; dθ=u[2]; du[1]=dθ; du[2]=-(g/L)*sin(θ))
+bc2(residual, ua, ub) = (residual[1] = ua[1] + pi/2; residual[2] = ub[1] + pi/2)
+bvp2 = TwoPointBVProblem(simplependulum, bc2, [pi/2,pi/2], (tspan[1],tspan[end]))
+sol2 = solve(bvp2, MIRK4(), dt=dtframe) # use the MIRK4 solver for TwoPointBVProblem
+
+# movie making background
+backdrop(scene, framenumber) = background(bgcolor)
+
+function frame(scene, framenumber)
+    u1, u2 = sol2.u[framenumber]
+    y, x = L*cos(u1), L*sin(u1)
+    sethue(leaderhue)
+    poly([Point(-4.0, 0.0), Point(4.0, 0.0),
+          Point(160.0x,160.0y)], :fill)
+    sethue(Colors.HSV(framenumber*4.0, 1, 1))
+    circle(Point(160.0x,160.0y), 160bobd, :fill)
+    text(string("frame $framenumber of $(scene.framerange.stop)"),
+        Point(0.0, -190.0),
+        halign=:center)
+end
+
+muv = Movie(400, 400, "Pendulum Demo", 1:length(tspan))
+animate(muv, [Scene(muv, backdrop),
+              Scene(muv, frame, easingfunction=easeinoutcubic)],
+              creategif=true, pathname=giffilename)

Task/Animate-a-pendulum/Lingo/animate-a-pendulum.lingo

@@ -0,0 +1,43 @@
+global RODLEN, GRAVITY, DT
+global velocity, acceleration, angle, posX, posY
+
+on startMovie
+
+    -- window properties
+    _movie.stage.title = "Pendulum"
+    _movie.stage.titlebarOptions.visible = TRUE
+    _movie.stage.rect = rect(0, 0, 400, 400)
+    _movie.centerStage = TRUE
+    _movie.puppetTempo(30)
+
+    RODLEN = 180
+    GRAVITY = -9.8
+    DT = 0.03
+
+    velocity = 0.0
+    acceleration = 0.0
+    angle = PI/3
+    posX = 200 - sin(angle) * RODLEN
+    posY = 100 + cos(angle) * RODLEN
+    paint()
+
+    -- show the window
+    _movie.stage.visible = TRUE
+end
+
+on enterFrame
+    acceleration = GRAVITY * sin(angle)
+    velocity = velocity + acceleration * DT
+    angle = angle + velocity * DT
+    posX = 200 - sin(angle) * rodLen
+    posY = 100 + cos(angle) * rodLen
+    paint()
+end
+
+on paint
+    img = _movie.stage.image
+    img.fill(img.rect, rgb(255,255,255))
+    img.fill(point(200-5, 100-5), point(200+5, 100+5), [#shapeType:#oval,#color:rgb(0,0,0)])
+    img.draw(point(200, 100), point(posX, posY), [#color:rgb(0,0,0)])
+    img.fill(point(posX-20, posY-20), point(posX+20, posY+20), [#shapeType:#oval,#lineSize:1,#bgColor:rgb(0,0,0),#color:rgb(255,255,0)])
+end

Task/Animate-a-pendulum/Ring/animate-a-pendulum.ring

@@ -0,0 +1,82 @@
+# Project : Animate a pendulum
+# Date    : 2018/04/09
+# Author : Gal Zsolt (~ CalmoSoft ~)
+# Email   : <calmosoft@gmail.com>
+
+load "guilib.ring"
+load "stdlib.ring"
+
+CounterMan = 1
+paint = null
+pi = 22/7
+theta = pi/180*40
+g = 9.81
+l = 0.50
+speed = 0
+
+new qapp
+        {
+        win1 = new qwidget() {
+                  setwindowtitle("Animate a pendulum")
+                  setgeometry(100,100,800,600)
+                  label1 = new qlabel(win1) {
+                              setgeometry(10,10,800,600)
+                              settext("")
+                  }
+                  new qpushbutton(win1) {
+                          setgeometry(150,500,100,30)
+                          settext("draw")
+                          setclickevent("draw()")
+                  }
+                  TimerMan = new qtimer(win1)
+                  {
+                                    setinterval(1000)
+                                    settimeoutevent("draw()")
+                                    start()
+                  }
+                  show()
+        }
+        exec()
+        }
+
+func draw
+        p1 = new qpicture()
+               color = new qcolor() {
+               setrgb(0,0,255,255)
+        }
+        pen = new qpen() {
+                 setcolor(color)
+                 setwidth(1)
+        }
+        paint = new qpainter() {
+                  begin(p1)
+                  setpen(pen)
+        ptime()
+        endpaint()
+        }
+        label1 { setpicture(p1) show() }
+        return
+
+ func ptime()
+         TimerMan.start()
+         pPlaySleep()
+         sleep(0.1)
+         CounterMan++
+         if CounterMan = 20
+            TimerMan.stop()
+         ok
+
+func pPlaySleep()
+       pendulum(theta, l)
+       pendulum(theta, l)
+       accel = - g * sin(theta) / l / 100
+       speed = speed + accel / 100
+       theta = theta + speed
+
+func pendulum(a, l)
+       pivotx = 640
+       pivoty = 800
+       bobx = pivotx + l * 1000 * sin(a)
+       boby = pivoty - l * 1000 * cos(a)
+       paint.drawline(pivotx, pivoty, bobx, boby)
+       paint.drawellipse(bobx + 24 * sin(a), boby - 24 * cos(a), 24, 24)