How can i make my ODE graph make sense?

I don't know why my graph is like that ! I tried to plot the differential and the solved ODE but my graph dont make sense.

I'm trying to make a graph of a ODE about a ball dropping in oil, the values are all random, just to plot the thing

clear; clc;

clearvars;

syms t v(t) aa g p p1

aa = 5;

u = 3;

g = 10

p1 = 9;

p = 3;

v0= 0;

cond = v(0) == v0

eqn = diff(v,t) == (1-p1/p)*g-(9*u/2*aa^2*p)*v

vSol(t)= simplify( dsolve(eqn,cond) )

fplot(t,vSol(t),[0 10000]); hold on; grid on;

Answer 1

[Star Strider]

The fplot call is incorrect, and the function declines so quickly that it’s not possible to see it clearly with a time interval going from 0 to 1E+5.

Correct those and it works!

syms t v(t) aa g p p1
aa = 5;
u = 3;
g = 10

g = 10

p1 = 9;
p = 3;
v0= 0;
cond = v(0) == v0

cond = 

eqn = diff(v,t) == (1-p1/p)*g-(9*u/2*aa^2*p)*v

eqn(t) = 

vSol(t)= simplify( dsolve(eqn,cond) )

vSol(t) = 

figure
fplot(vSol(t),[0 1E-2]); hold on; grid on;

.

[Ian Samuelsson]

i totaly understand, thank you soo mutch !!!!!

[Star Strider]

As always, my pleasure!

.

[Ian Samuelsson]

@Star Strider sorry to bothering you, you did help me a lot, but now i was trying to plot a vetorial camp to show the flow with quiver, but i dont know what im doing wrong

syms t v(t) aa g p p1

%alpha = r

aa = 5;

%u=mi

u = 3;

%gravity

g = 10

%density'

p1 = 9;

%density

p = 3;

v0= 0;

cond = v(0) == v0

eqn = diff(v,t) == (1-p1/p)*g-(9*u/2*aa^2*p)*v

vSol(t)= simplify( dsolve(eqn,cond) )

fplot(vSol(t),[0 1E-2]); hold on; grid on;

ang = atan(eqn(V,T));

xx = linspace (-5, 5 , 30); yy=xx;

[V,T]= meshgrid(xx,yy);

U= cos(ang);

V= sin(ang);

quiver(X,Y,U,V); hold on; grid on;

%quiver(t, v(t), [0 10 100]);

i tried to make the arrows with quiver, but i dont know why this is a failure, i make in xx and yy just to separate the main things, i dont know if the problem is that everything is with respect to t.

[Star Strider]

No worries!

The quiver function wants numerical values, not symbolic values, and those are easily provided.

I’m not certain what the desired result is, however I created some results that might be close to it. If they’re not, please describe in detail what the desired result is, and I’ll do my best to help provide it.

syms t v(t) aa g p p1
%alpha = r
aa = 5;
%u=mi
u = 3;
%gravity
g = 10

g = 10

%density'
p1 = 9;
%density
p = 3;

v0= 0;
cond = v(0) == v0

cond = 

eqn = diff(v,t) == (1-p1/p)*g-(9*u/2*aa^2*p)*v

eqn(t) = 

vSol(t)= simplify( dsolve(eqn,cond) )

vSol(t) = 

fplot(vSol(t),[0 1E-2]); hold on; grid on;
Ax = gca;
% get(Ax)
T = Ax.Children.XData;                                      % Get Data From Plot
V = Ax.Children.YData;                                      % Get Data From Plot


ang = atan2(V,T);                                           % Use Four-Quadrant Arctangent
% xx = linspace (-5, 5 , 30); yy=xx;
% [V,T]= meshgrid(xx,yy);
% Uq= cos(ang);
% Vq= sin(ang);
Uq = gradient(T);                                           % Numerical Derivative
Vq = gradient(V);                                           % Numerical Derivative
quiver(T,V,Uq,Vq); hold on; grid on;

%quiver(t, v(t), [0 10 100]);

Experimment to get the desired result.

.

[Ian Samuelsson]

Man, i apreciate your help but look what i got, i make my quiver and meshgrid show me the gradient, i got what i want, now i'm trying adjust the scale.

syms t v(t) aa g p p1

%alpha = r

aa = 3;

%u=mi

u = 1;

%gravity

g = 10

%fluid density

p1 = 2;

%density

p = 1.5;

v0= 0;

cond = v(0) == v0

eqn = diff(v,t) == (1-p1/p)*g-(9*u/2*aa^2*p)*v

vSol(t)= simplify( dsolve(eqn,cond) )

fplot(vSol(t),[0 1E-2]); hold on; grid on;

xx = linspace (0, 1E-4 , 10);

yy = vSol(xx);

[X,Y]= meshgrid(xx,yy);

% ang = atan(eqn(X,Y));

% U = cos(ang);

% V = sin(ang);

quiver(X,Y); hold on; grid on;

%quiver(t, v(t), [0 10 100]);

[Star Strider]

syms t v(t) aa g p p1
%alpha = r
aa = 3;
%u=mi
u = 1;
%gravity
g = 10

g = 10

%fluid density
p1 = 2;
%density
p = 1.5;

v0= 0;
cond = v(0) == v0

cond = 

eqn = diff(v,t) == (1-p1/p)*g-(9*u/2*aa^2*p)*v

eqn(t) = 

vSol(t)= simplify( dsolve(eqn,cond) )

vSol(t) = 

fplot(vSol(t),[0 1E-2]); hold on; grid on;

xx = linspace (0, 1E-4 , 10);
yy = vSol(xx);
[X,Y]= meshgrid(xx,yy);
% ang = atan(eqn(X,Y));
% U = cos(ang);
% V = sin(ang);
quiver(X,Y); hold on; grid on;

I don’t understand the problem. Perhaps Disable Automatic Scaling will do what you want.

.

[Ian Samuelsson]

is a ODE :

[A body falling in a relatively dense fluid, oil for example, is acted on by three forces (see Figure 2.3.5): a resistive force R, a buoyant force B, and its weight w due to gravity. The buoyant force is equal to the weight of the fluid displaced by the object. For a slowly moving spherical body of radius a, the resistive force is given by Stokes’s law, R = 6πµa|v|, where v is the velocity of the body, and µ is the coefficient of viscosity of the surrounding fluid...]

i finish everything, i'm just suferying in the graphs ahahahah.

@Star Strider About the disable is just turn off the hold ? putting hold off ? i did not understand that part.

[Star Strider]

The hold condition can be toggled on or off depending on whether other data are to be plotted to the same axes, or not.