GRAPH, samples

Physical samples drawn with GRAPH

RLC-filter.

xmax=35; roots=0; L=1; C=0.005; U0=1; Rc=-i/(w*C) R=1+i*w*L R3=Rc*(R+Rc)/(R+2*Rc) R2=Rc*(R+R3)/(Rc+R+R3) R1=Rc*(R+R2)/(Rc+R+R2) R=R+R1 U1=U0*R1/(R+R1) U2=U1*R2/(R+R2) U3=U2*R3/(R+R3) Uout(w)=abs(U3*Rc/(R+Rc)) U=abs(U3*Rc/(R+Rc));
xmin=0.1, xmax=35, fmin=0, fmax=40

Uo   >-R--L--|--R--L--|--R--L--|--R--L--|--->Uout(w)
             |        |        |        |  
             C        C        C        C   
             |        |        |        |  
Земля o--------------------------------------o

Eliptical orbit with eccentricity 0.8

xmax=2*pi; ratio=1 0.1/(1.0+0.8*cos(x))*exp(i*x) f=0.1/(1.0+0.8*cos(x))*exp(i*x); xmin=0, xmax=6.28
fmin=(-0.5 + i*-0.185),
fmax=(0.0556 + i*0.185)

Lissajous figures



k=3

fi=2

a1=sin(t)

a2=sin(k*t+fi) 

XY(t)=a1+i*a2

XY=a1+i*a2; xmin=0, xmax=6.28318530717959
fmin=(-1 - i), fmax=(1 + i)

AM & FM signals.

f=(1+b*cos(a*t))*cos(w0*t); xmin=0, xmax=314.159265358979; fmin=-1.1984229402629, fmax=1.2

f=cos(w0*t+b*sin(a*t)); xmin=0, xmax=314.159265358979; fmin=-1, fmax=1

xmax=100*pi roots=0; width=800; points=800; fbox=0 a=0.04; b=0.2; w0=1 f(t)=(1+b*cos(a*t))*cos(w0*t) %%АМ xmax=100*pi roots=0; width=800; points=800; fbox=0 a=0.04; b=15; w0=1 f(t)=cos(w0*t+b*sin(a*t)) %%ФМ

Resonance circuit.

Resonance curve I(w): `xmin=1 L=1; C=0.1; R=1; U=1 %%Circuit parameters rL=iwL %%Impedance of inductance rC= -i/(w*C) %%Impedance of capacity I(w)=abs(U/(R+rL+rC)) %%Current in a circuit`	I=abs(U/(R+rL+rC)); xmin=1, xmax=6.28 fmin=0.110431526074847, fmax=0.999970724714332
Phase characteristic of a circuit Fi(w): `xmin=1 L=1; C=0.1; R=1; U=1 rL=iwL rC= -i/(w*C) I=U/(R+rL+rC) a=Im(I); b=Re(I) %%Real and complex part of current Fi(w)=atan(a/b) %%Phase shift between current and voltage`	Fi=atan(a/b); xmin=1, xmax=6.28 fmin=-1.36079362306812, fmax=1.460139105621 Корни: 3.16227766016838
Phase shift between voltage and current. `xmax=1; roots=0; ratio=0 w=2pi %%w is an angle frequency L=1; C=0.1; R=1 U=exp(iwt) %%t is the time rL=iwL rC= -i/(wC) I=U/(R+rL+rC) XY(t)=cplx(Re(U),Re(I))`	XY=cplx(Re(U),Re(I)); xmin=0, xmax=1 fmin=(-1 + i-0.208), fmax=(1 + i0.208)

Fabry-Perot interferometer

Reflection from Fabry-Perot interferometer.
Bottom curve is glass plate. Reflection of the glass surface is 4%. Total reflection of the plate in resonance is ~55%.

nmax=5; animated(100,1) points=200; width=400 xmin=-10; xmax=10; fmin=0 I0=1; R=0.04+0.2*n; r=sqrt(R) Id(fi)=I0*4*r*(sin(fi/2))**2/((1-r)**2+4*r*(sin(fi/2))**2)

Id=I0*4*r*(sin(fi/2))**2/((1-r)**2+4*r*(sin(fi/2))**2);
xmin=-10, xmax=10, fmin=0 , fmax=0.998

Transmission of Fabry-Perot interferometer.

nmax=5; animated(100,1) points=200; width=400 xmin=-10; xmax=10; fmin=0 I0=1; R=0.04+0.2*n; r=sqrt(R) Id(fi)=I0*(1-r)**2/((1-r)**2+4*r*(sin(fi/2))**2)

Id=I0*(1-r)**2/((1-r)**2+4*r*(sin(fi/2))**2);
xmin=-10, xmax=10, fmin=0 , fmax=1

Plank distribution

Plank distribution of the energy of radiation of the absolutely black body independence on the wavelength and frequency of the light. Wavelength region is 1...30 microns. There are in the graph several curves which differ by temperature. nmax=5. Variable n is changed from 0 to nmax-1.

radiation of the black body on the frequency of the light. Maximal frequency corresponds wavelength 3 microns. Temperature is changed from 60 to 300 К, wth the aid of parameter n. roots=0; nmax=5 h=6.62e-27 c=2.99e+10 T=300*(n+1)/nmax k=1.38e-16 lambda=3 xmin=1; xmax=2*pi*c*1000/lambda ro(nu)=8*pi*h*nu^3/(c^3*(exp((h*nu)/(k*T))-1)) ro=8*pi*h*nu**3/(c**3*(exp((h*nu)/(k*T))-1));
xmin=1, xmax=62622413561556.5
fmin=7.78e-45, fmax=2.16e-18

Radiation of the black body in the wavelength region from 1 to 30 microns.

roots=0; nmax=5 xmin=1; xmax=30 h=6.62e-27 c=2.99e+10 l=x*1e-4 T=300*(n+1)/nmax k=1.38e-16 f=(8*pi*h*c/(l^5))*(1/(exp(h*c/(k*T*l))-1))

f=(8*pi*h*c/(l**5))*(1/(exp(h*c/(k*T*l))-1));
xmin=1, xmax=30
fmin=7.52e-99, fmax=0.0422

Brownian motion

Position of the point on the plane can be animated. In the next sample we used for this a generator of the random numbers in the range from 0 to 0.1 - rand(0.1). The position of a "particle" is stored in a variables a and b.

nmax=200; animated(10,0) xmax=1; xmin=-1; ymax=1; ymin=-1 begin points 0 0 end x=a+rand(0.1)-0.05 y=b+rand(0.1)-0.05 a=x b=y

xmin=-1, xmax=1, fmin=-1, fmax=1

Rotation of geosphere.

nmax=20; animated(10,0) xmin=-12; xmax=12 ymin=-12; ymax=12 width=200 ... точки сферы (см. свойства рисунка) fi=pi*n/(6*nmax) (x,y,z)=z_rotate(x,y,z,fi) (x,y,z)=x_rotate(x,y,z,pi/4)Presence inv in the body of the code makes the rare points (z<0) invisible. xmin=-12, xmax=12, fmin=-12, fmax=12

Physical and mathematical package "GRAPH"

Resonance curve I(w): `xmin=1 L=1; C=0.1; R=1; U=1 %%Circuit parameters rL=iwL %%Impedance of inductance rC= -i/(w*C) %%Impedance of capacity I(w)=abs(U/(R+rL+rC)) %%Current in a circuit`	I=abs(U/(R+rL+rC)); xmin=1, xmax=6.28 fmin=0.110431526074847, fmax=0.999970724714332
Phase characteristic of a circuit Fi(w): `xmin=1 L=1; C=0.1; R=1; U=1 rL=iwL rC= -i/(w*C) I=U/(R+rL+rC) a=Im(I); b=Re(I) %%Real and complex part of current Fi(w)=atan(a/b) %%Phase shift between current and voltage`	Fi=atan(a/b); xmin=1, xmax=6.28 fmin=-1.36079362306812, fmax=1.460139105621 Корни: 3.16227766016838
Phase shift between voltage and current. `xmax=1; roots=0; ratio=0 w=2pi %%w is an angle frequency L=1; C=0.1; R=1 U=exp(iwt) %%t is the time rL=iwL rC= -i/(wC) I=U/(R+rL+rC) XY(t)=cplx(Re(U),Re(I))`	XY=cplx(Re(U),Re(I)); xmin=0, xmax=1 fmin=(-1 + i-0.208), fmax=(1 + i0.208)