193
Tabiatda real holda barcha erkin tebranishlar so‘nuvchi bo‘ladi. Mayatniklar,
elektromagnit tebranish konturi va boshqa tebranuvchi sistemalarda so‘nishning
oldini olish uchun majburiy tebranish hosil qilinishi ya’ni tashqi davriy kuch
ta’siri, qo‘shimcha energiya manbai kerak bo‘ladi. Quyida so‘nuvchi garmonik
tebranma harakat siljish masofasini vaqtga bog‘lanish
tenglamasini kompyuter
dasturlari orqali grafigini o‘rganamiz.
a)
MATLAB dasturiy tizimida:
sm
A 10
=
,
cek
rad /
4
=
,
125
.
0
=
,
6
0
=
qiymatlari
uchun so‘nuvchi tebranma harakat tenglamasi
sm
t
e
x
t
)
6
4
sin(
10
02
.
0
+
=
−
ko‘rinishga
keladi. Tezlikning vaqtga bog‘lanish tenglamasini
dt
dx
=
,
tezlanishning vaqtga
bog‘lanish tenglamasini esa
2
2
dt
x
d
dt
d
a
=
=
differensial tenglamani yechish orqali
amalga oshiriladi. Siljish masofasi, tezlik, tezlanishlarning vaqtga bog‘liqlik
grafigini chiziladi.
x=sym('10*exp(-
0.125*t)*sin(pi/4*t+pi/6)')
x =(10*sin(pi/6 +
(pi*t)/4))/exp(0.125*t)
v=diff(x,'t')
v =(5*pi*cos(pi/6 +
(pi*t)/4))/(2*exp(0.125*t)) -
(1.25*sin(pi/6 +
(pi*t)/4))/exp(0.125*t)
v=sym('(5*pi*cos(pi/6 +
(pi*t)/4))/(2*exp(0.125*t)) -
(1.25*sin(pi/6 +
(pi*t)/4))/exp(0.125*t)')
v =(5*pi*cos(pi/6 +
(pi*t)/4))/(2*exp(0.125*t)) -
(1.25*sin(pi/6 +
(pi*t)/4))/exp(0.125*t)
a=diff(v,'t')
a =(0.15625*sin(pi/6 +
(pi*t)/4))/exp(0.125*t) -
(0.625*pi*cos(pi/6 +
(pi*t)/4))/exp(0.125*t) -
(5*pi^2*sin(pi/6 +
(pi*t)/4))/(8*exp(0.125*t))
a=sym('(0.15625*sin(pi/6
+ (pi*t)/4))/exp(0.125*t) -
(0.625*pi*cos(pi/6 +
(pi*t)/4))/exp(0.125*t) -
(5*pi^2*sin(pi/6
+
(pi*t)/4))/(8*exp(0.125*t))')
a=(0.15625*sin(pi/6 +
(pi*t)/4))/exp(0.125*t) -
(0.625*pi*cos(pi/6 +
(pi*t)/4))/exp(0.125*t) -
(5*pi^2*sin(pi/6 +
(pi*t)/4))/(8*exp(0.125*t))
ezplot(x,[0,20])
ezplot(v,[0,20])
ezplot(a,[0,20])
194
b) Dev-C++ dasturlash tilida: Dev-C++
dasturida dasturlash amalga
oshirish jarayonida funksiyaning argumentga bog‘lanish tenglamasini kiritishda
qulaylik uchun MATLAB dasturiy tizimida yozilgan dastur tarkibidan nusxa olish
maqsadga muvofiq. Dasturlash jarayonida masshtabni, koordinatalar boshini va
ketma-ketlik
koeffitsiyenti k ni to‘g‘ri tanlash lozim. Shuni ta’kidlash joizki,
MATLAB dasturiy tizimida matematik amallarni bajarish, masala yechimini
topish, grafiklarni chizish, so‘ngra Dev-C++ (4.9.9.2) dasturlash tilida avval grafik
rejimga o‘tish va dasturlashni amalga oshirish kerak bo’ladi. Kompilyatsiya
jarayonini amalga oshirganimizdan so’ng grafik chizish Dev-C++
da Console
oynasida qora chiziqlar orqali amalga oshiriladi.
#include
#include
#include
#include
using namespace std;
int main()
{
initwindow(600,400);
setbkcolor(WHITE);
clearviewport();
setcolor(BLACK);
line(0,200,getmaxx(),2
00);
line(300,0,300,getmax
y());
double
x,y,i,pi=3.14,k=0.1;
for(int i=-
250;i<300;i=i+1)
{
x=250+i;
y=200-10*(exp(-
0.125*k*i))*sin(pi/4*k*i+pi/6);
putpixel(x,y,BLACK);
y =200-(2.5*pi*cos(pi/6+pi/4*k*i)*exp(-
0.125*k*i)-(1.25*sin(pi/6+pi/4*k*i))*exp(-
0.125*k*i));
putpixel(x,y,BLACK);
y=200-(0.15625*sin(pi/6+pi/4*k*i)*exp(-
0.125*k*i)-0.625*pi*cos(pi/6+pi/4*k*i)*exp(-
0.125*k*i)-
5*pi*pi*sin(pi/6+pi/4*k*i)/(8*exp(0.125*k*i)));
putpixel(x,y,BLACK);
delay(10);
}
getch();
closegraph();
return 0;
}
Fizikaviy jarayonlarni dasturlash tillaridan foydalanib o‘rganish kelajakda
yosh dasturchidan mukammal dasturlarni yaratishida asos bo‘ladi. Fizikadan
amaliy mashg‘ulot jarayonida zamonaviy axborot texnologiyalaridan foydalanish,
0
2
4
6
8
10
12
14
16
18
20
-6
-4
-2
0
2
4
6
8
t (s)
X = (10 sin(
/6 + (
t)/4))/exp(0.125 t)
X
195
xususan MATLAB, MAPLE, MathCAD dasturiy tizimlari hamda Dev-C++,
Java(SE-8)-eclipse kompyuter dasturlarini samarali grafik rejimda qo‘llanilishi
o‘quvchi amaliy faoliyatini faollashtirishtiradi hamda dastulash tillarini chiqur
o’zlashtirishida amaliy yordam beradi.
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