simple pendilum

[tsh73]

Now for some magic

take a 1 meter of thread
put a weight on one end
hold other end in your arm

Run program below

Then you get used to drawn pendilum swinging, release weight in real thread pendilum so they start swing on same time moment.

Now, real (thread) pendilum and drawn (JustBASIC) pendilum swing in sync.

Isn't that nice?
'simple pendilum

nomainwin
WindowHeight=720
WindowWidth=720
UpperLeftX=1
UpperLeftY=1
pi=acs(-1)

open "simple pendilum" for graphics_nsb_nf as #gr
#gr "trapclose [quit]"
#gr "down"
'#gr "fill white; flush"
#gr "home; posxy cx cy"

DPI=144 'set your own
sc = DPI/2.54*100    'scale, dpi -> dpCm -> dpMeter
'this is likely real scale
'now decrease it
'sc =sc /100 '1:100, 1 meter in 1 cm
'sc =sc /1000 '1:1000, 1 meter in 1 mm
sc =sc /10 '1:10, 1 meter in 10 cm of screen
'notice sc   '567 pixels in 10 cm of screen

'pendilum
g=9.8   'Earth
'g=9.8/6   'Moon

L=1 '1 meter, scaled by sc

R=0.0254 'r=1 in
R=0.05 'r=5 cm

A=15*pi/180 'amplitude

'pivot
x00=cx:y00=40
#gr "place ";x00;" ";y00
x=x00:y=y00+L*sc
#gr "goto ";x;" ";y
#gr "circle ";R*sc

'equation
'1) simple pendulum for small alpha
'small angle, sin a = a (radians)
'got to
'alph(t)=sin(sqr(g/L)*t)

timer 1, [tick] 'minimal possible
t0=time$("ms")
wait

[tick]
   t1=time$("ms")
   dt=(t1-t0)/1000  'so how much time passed?
   a=A*sin(sqr(g/L)*dt)
   #gr "cls"
   #gr "place ";x00;" ";y00
   x=x00+L*sc*sin(a):y=y00+L*sc*cos(a)
   #gr "goto ";x;" ";y
   'print dt, a, x, y
   #gr "circle ";R*sc

wait

[quit]
timer 0
close #gr
end


[B+]

We were able to run a sim of this: www.reddit.com/r/BetterEveryLoop/comments/j0sdgz/slightly_different_string_lengths_cause_patterns/?utm_source=share&utm_medium=ios_app&utm_name=iossmf

at another forum. Maybe we could take a shot at it here?

[B+]

Ah here it is with a little mod!
' ref: https://www.qb64.org/forum/index.php?topic=3056.msg123288#msg123288
' by FellippeHeitor ported to JB and modified by bplus 2020-12-23

Global Xmax, Ymax, Pi, maxPendulum
Xmax = 1100 : Ymax = 600 : Pi = acs(-1) : maxPendulum = 15

'SCREEN _NEWIMAGE(1000, 600, 32)
'CONST maxPendulum = 15
'DIM g, i AS INTEGER
DIM Theta(maxPendulum), Accel(maxPendulum), Speed(maxPendulum)
DIM Length(maxPendulum), Mass(maxPendulum)
'DIM px, py, bx, by
g = 9.81
FOR i = 0 TO maxPendulum
   Theta(i) = Pi / 1.5
   Speed(i) = 0
   Length(i) = 100 + i * 30
   Mass(i) = 1 - i * .01
NEXT

'px = _WIDTH / 2
px = Xmax /2
py = 0

'DO UNTIL _SCREENEXISTS: _LIMIT 1: LOOP
'_TITLE "Pendula"

nomainwin

WindowWidth = Xmax + 8
WindowHeight = Ymax + 32
UpperLeftX = (1200 - Xmax) / 2  'or delete if XMAX is 1200 or above
UpperLeftY = (700 - Ymax) / 2   'or delete if YMAX is 700 or above

open "Pendula by FellippeHeitor port to JB and modified by bplus" for graphics_nsb_nf as #gr
#gr "setfocus"
#gr "trapclose Quit"
#gr "when leftButtonUp lButtonUp"
'#gr "when characterInput charIn"
#gr "down"
#gr "fill black"
'DO
#gr "color white"
while 1
   scan
   'CLS
   #gr "fill black"
   'WHILE _MOUSEINPUT: WEND  ' see mouse handler event
   FOR i = 1 TO maxPendulum
       'IF _MOUSEBUTTON(1) THEN  'check mouse click
           'theta(i) = map(_MOUSEX, 0, _WIDTH - 1, 4.7, 1.57)
           'speed(i) = 0
       'ELSE
           Accel(i) = Mass(i) * g * SIN(Theta(i)) / 100
           Speed(i) = Speed(i) + Accel(i) / 100
           Theta(i) = Theta(i) + Speed(i)
       'END IF
       bx = px + Length(i) * SIN(Theta(i))
       by = py - Length(i) * COS(Theta(i))
       'LINE (px, py)-(bx, by), c(i)
       #gr "line ";px;" ";py;" ";bx;" ";by
       'CircleFill bx, by, map(i, 0, maxPendulum, 20, 40), c(i)
       if i mod 2 then #gr "backcolor red" else #gr "backcolor darkgreen"
       #gr "place ";bx;" ";by;"; circlefilled ";20
       #gr "place ";bx-4;" ";by+4;";|";mid$("Merry Christmas", i, 1)
   NEXT
   '_DISPLAY  'gotta live with the blinking
   '_LIMIT 60
   call Pause 40  'any less Pause is blinky, if you get too much blick raise the Pause number
'LOOP
wend
wait

FUNCTION Map (value, minRange, maxRange, newMinRange, newMaxRange)
   Map = ((value - minRange) / (maxRange - minRange)) * (newMaxRange - newMinRange) + newMinRange
END FUNCTION

sub lButtonUp H$, mx, my  'must have handle and mouse x,y
   FOR i = 1 to maxPendulum
       'theta(i) = map(_MOUSEX, 0, _WIDTH - 1, 4.7, 1.57)
       Theta(i) = Map(mx, 0, Xmax, 4.7, 1.57)
       Speed(i) = 0
   next
end sub

sub Quit H$
   close #gr '<=== this needs Global H$ = "gr" < blah never works right!
   end
end sub

sub Pause mil   'tsh version has scan built-in
   t0 = time$("ms")
   while time$("ms") < t0 + mil : scan : wend
end sub



Hmm... takes a little longer to set up patterns because if try to speed Pauses the blinking gets too annoying.

Attachments:

[code]

Pretty cool both... thx for sharing !

[tsh73]

Wow wow!

Such a nice real physics (first link video)!
Such a nice animation! (program)

As for blinking probably sprites could help, one has to try.
(of course I set pause to minimum :))

Now I look inside - it has real differential equation.
Me thinks it will look more "real" if initial amplitude will be smaller. Like
Theta(i) = Pi / 1.1
instead of
Theta(i) = Pi / 1.5

It really looks rotating in 3d, and green disks looks transparent glass with all that white threads shining through.

But it looks like there is some corners cut in a math.
Pendulum frequency should not depend on a mass - but here masses are different,
and if I make mass the same, all balls go with same frequency.
(probably masses compensate for equation on angle do not accounting for thread length)

Looks really real anyway

Btw if you wait long enough, red balls separate and say

M r y C r s m s

- perfectly recognizable!

Btw2
increasing "g" value makes it runs faster.
Like, g = g*10

Btw3 (sorry)
#gr "discard"
in the loop prevents graphic memory build-up, thus making it faster

[Rod]

Yes super cool, and thanks to Anatoly for the inspiration. You both make this forum really interesting and worthwhile.

[B+]

Thanks Rod

and tsh73 for 2 of the 3 BTW's, a higher g sounds good and I always forget about #gr "discard".