how can I solve this problem

v=0.001;        
L=0.084;   
D=0.042;     
R=0.02;     
C=0.001;
sm= v*N*L*R*L^2/(4*W*C^2);
sm=(1-p^2)^2/p*((16*p^2+pi^2*(1-p^2))^0.5;
p=?

Answer 1

[Star Strider]

I have no idea what you want, especially with two expressions for ‘sm’ and several variables undefined, so taking a wild guess —

syms N W p 
sympref('AbbreviateOutput',false);
v=0.001;        
L=0.084;   
D=0.042;     
R=0.02;     
C=0.001;
sm1 = v*N*L*R*L^2/(4*W*C^2);
sm = (1-p^2)^2/p*(16*p^2+pi^2*(1-p^2))^0.5 == sm1;
ps = solve(sm, p, 'ReturnConditions',1)

ps = struct with fields:
             p: [10×1 sym]
    parameters: [1×0 sym]
    conditions: [10×1 sym]

p = ps.p

p = 

condx = ps.conditions

condx = 

To get a numerical result, supply values for the currently undefined variables, then one of these:

p = vpa(ps.p)

p = double(ps.p)

depending on the desired result.

EDIT — Corrected typographical error. .

[Gloria]

Thank you for the answer ;

I asked the question wrong actually. I am trying the draw sommerfeld number-eccentricity graph.

The x-axis of the graph is between 0 and 1 which is given with "p", and the y-axis is the equation "(1-p^2)^2/p*(16*p^2+pi^2*(1-p^2))^0.5" that depends on the p. How can I draw this graph?

[Star Strider]

With the missing variables supplied, one approach to drawing the plot would be:

sm1 = v*N*L*R*L^2/(4*W*C^2);
sm(p) = (1-p^2)^2/p*(16*p^2+pi^2*(1-p^2))^0.5 - sm1;

figure
fplot(sm, [0 1])
grid

See the documentation for fplot for more infoormation on it.

Another option (not using the Symbolic Math Toolbox) would be —

v=0.001;        
L=0.084;   
D=0.042;     
R=0.02;     
C=0.001;
N = ;                                                       % Provide This Value
W = ;                                                       % Provide This Value
sm1 = v*N*L*R*L^2./(4*W*C^2);
sm = @ (p) (1-p.^2).^2./p.*sqrt(16*p.^2+pi^2.*(1-p.^2)) - sm1;
p = linspace(0, 1, 250);

figure
plot(p, sm(p))
grid

.

[Gloria]

Thank you so much

[Star Strider]

My pleasure!

I still don’t understand how best to reconcile or combine the two expressions for ‘sm’. I ended up subtracting them because the original intent was to find ‘p’, however I still wonder what the intent is now.

.

[Gloria]

Yes , in the first question I was trying to find "p" but later I realized that I understood the problem wrong.

I am trying the draw sommerfield number-eccentricity graph.

Thank you so much for your time.

[Star Strider]

My pleasure!

Answer 2

[Matt J]

Are N and W known variables? Your code does not provide them, but if they are known, you can reorganize as a polynomial and use roots,

v=0.001;        
L=0.084;   
D=0.042;     
R=0.02;     
C=0.001;
N=1;W=1; %fake
sm= v*N*L*R*L^2/(4*W*C^2);

syms p


pol=sym2poly( sm^2*p^2*(16*p^2+pi^2*(1-p^2))  - (1-p^2)^4 )

pol = 1×9

-1.0000 0 4.0000 0 -5.9999 0 4.0001 0 -1.0000

p=roots(pol) %the solutions

p = 
  -1.0550 + 0.0000i
  -0.9994 + 0.0544i
  -0.9994 - 0.0544i
  -0.9461 + 0.0000i
   1.0550 + 0.0000i
   0.9994 + 0.0544i
   0.9994 - 0.0544i
   0.9461 + 0.0000i