Task: Animate a pendulum







Python: import pygame, sys
from pygame.locals import *
from math import sin, cos, radians

pygame.init()

WINDOWSIZE = 250
TIMETICK = 100
BOBSIZE = 15

window = pygame.display.set_mode((WINDOWSIZE, WINDOWSIZE))
pygame.display.set_caption("Pendulum")

screen = pygame.display.get_surface()
screen.fill((255,255,255))

PIVOT = (WINDOWSIZE/2, WINDOWSIZE/10)
SWINGLENGTH = PIVOT[1]*4

class BobMass(pygame.sprite.Sprite):
    def __init__(self):
        pygame.sprite.Sprite.__init__(self)
        self.theta = 45
        self.dtheta = 0
        self.rect = pygame.Rect(PIVOT[0]-SWINGLENGTH*cos(radians(self.theta)),
                                PIVOT[1]+SWINGLENGTH*sin(radians(self.theta)),
                                1,1)
        self.draw()

    def recomputeAngle(self):
        scaling = 3000.0/(SWINGLENGTH**2)

        firstDDtheta = -sin(radians(self.theta))*scaling
        midDtheta = self.dtheta + firstDDtheta
        midtheta = self.theta + (self.dtheta + midDtheta)/2.0

        midDDtheta = -sin(radians(midtheta))*scaling
        midDtheta = self.dtheta + (firstDDtheta + midDDtheta)/2
        midtheta = self.theta + (self.dtheta + midDtheta)/2

        midDDtheta = -sin(radians(midtheta)) * scaling
        lastDtheta = midDtheta + midDDtheta
        lasttheta = midtheta + (midDtheta + lastDtheta)/2.0
        
        lastDDtheta = -sin(radians(lasttheta)) * scaling
        lastDtheta = midDtheta + (midDDtheta + lastDDtheta)/2.0
        lasttheta = midtheta + (midDtheta + lastDtheta)/2.0

        self.dtheta = lastDtheta
        self.theta = lasttheta
        self.rect = pygame.Rect(PIVOT[0]-
                                SWINGLENGTH*sin(radians(self.theta)), 
                                PIVOT[1]+
                                SWINGLENGTH*cos(radians(self.theta)),1,1)


    def draw(self):
        pygame.draw.circle(screen, (0,0,0), PIVOT, 5, 0)
        pygame.draw.circle(screen, (0,0,0), self.rect.center, BOBSIZE, 0)
        pygame.draw.aaline(screen, (0,0,0), PIVOT, self.rect.center)
        pygame.draw.line(screen, (0,0,0), (0, PIVOT[1]), (WINDOWSIZE, PIVOT[1]))

    def update(self):
        self.recomputeAngle()
        screen.fill((255,255,255))
        self.draw()

bob = BobMass()

TICK = USEREVENT + 2
pygame.time.set_timer(TICK, TIMETICK)

def input(events):
    for event in events:
        if event.type == QUIT:
            sys.exit(0)
        elif event.type == TICK:
            bob.update()

while True:
    input(pygame.event.get())
    pygame.display.flip()




Fortran: 
program animated_pendulum
implicit none
double precision, parameter :: pi = 4.0D0*atan(1.0D0), l = 1.0D-1, dt = 1.0D-2, g = 9.8D0
integer :: io
double precision :: s_ang, c_ang, p_ang, n_ang

write(*,*) 'Enter starting angle (in degrees):'
do
  read(*,*,iostat=io) s_ang
  if(io.ne.0 .or. s_ang.lt.-90.0D0 .or. s_ang.gt.90.0D0) then
    write(*,*) 'Please enter an angle between 90 and -90 degrees:'
  else
    exit
  end if
end do
call execute_command_line('cls')

c_ang = s_ang*pi/180.0D0
p_ang = c_ang

call display(c_ang)
do
  call next_time_step(c_ang,p_ang,g,l,dt,n_ang)
  if(abs(c_ang-p_ang).ge.0.05D0) then
    call execute_command_line('cls')
    call display(c_ang)
  end if
end do
end program

subroutine next_time_step(c_ang,p_ang,g,l,dt,n_ang)
double precision :: c_ang, p_ang, g, l, dt, n_ang
n_ang = (-g*sin(c_ang)/l)*2.0D0*dt**2 + 2.0D0*c_ang - p_ang
p_ang = c_ang
c_ang = n_ang
end subroutine

subroutine display(c_ang)
double precision :: c_ang
character (len=*), parameter :: cfmt = '(A1)'
double precision :: rx, ry
integer :: x, y, i, j
rx = 45.0D0*sin(c_ang)
ry = 22.5D0*cos(c_ang)
x = int(rx)+51
y = int(ry)+2
do i = 1,32
  do j = 1,100
    if(i.eq.y .and. j.eq.x) then
      write(*,cfmt,advance='no') 'O'
    else if(i.eq.y .and. (j.eq.(x-1).or.j.eq.(x+1))) then
      write(*,cfmt,advance='no') 'G'
    else if(j.eq.x .and. (i.eq.(y-1).or.i.eq.(y+1))) then
      write(*,cfmt,advance='no') 'G'
    else if(i.eq.y .and. (j.eq.(x-2).or.j.eq.(x+2))) then
      write(*,cfmt,advance='no') '#'
    else if(j.eq.x .and. (i.eq.(y-2).or.i.eq.(y+2))) then
      write(*,cfmt,advance='no') 'G'
    else if((i.eq.(y+1).and.j.eq.(x+1)) .or. (i.eq.(y-1).and.j.eq.(x-1))) then
      write(*,cfmt,advance='no') '#'
    else if((i.eq.(y+1).and.j.eq.(x-1)) .or. (i.eq.(y-1).and.j.eq.(x+1))) then
      write(*,cfmt,advance='no') '#'
    else if(j.eq.50) then
      write(*,cfmt,advance='no') '|'
    else if(i.eq.2) then
      write(*,cfmt,advance='no') '-'
    else
      write(*,cfmt,advance='no') ' '
    end if
  end do
  write(*,*)
end do
end subroutine