Hello, how to solve this equation E*I*k^4-m*v^2*k^2+2*m*v*w*k+(m+M)w^2=0 numerically where w is variable,
2 views (last 30 days)
Show older comments
shoaib Shoaib
on 10 Dec 2019
Commented: shoaib Shoaib
on 12 Dec 2019
can we solve this for k numerically, sorry this is fourth order equation not two order
Thanks
0 Comments
Accepted Answer
Star Strider
on 10 Dec 2019
Edited: Star Strider
on 10 Dec 2019
Supply all the scalar parameters, then:
Eqn = @(w) E*I*k^2-m*v^2*k^2+2*m*v*w*k+(m+M)w^2;
w0 = 42;
[w,fval] = fsolve(Eqn, w0)
Experiment with the correct value of ‘w0’ to get the correct result.
EDIT — (Dec 10 2019 at 13:18)
The Symbolic Math Toolbox produces:
w = (k*(- E*I*k^2*m - E*I*M*k^2 + 2*m^2*v^2 + M*m*v^2)^(1/2) - k*m*v)/(M + m)
or to calculate both roots:
w = [(k*(- E*I*k^2*m - E*I*M*k^2 + 2*m^2*v^2 + M*m*v^2)^(1/2) - k*m*v)/(M + m)
-(k*(- E*I*k^2*m - E*I*M*k^2 + 2*m^2*v^2 + M*m*v^2)^(1/2) - k*m*v)/(M + m)]
11 Comments
Walter Roberson
on 12 Dec 2019
syms E I k m v w M
Eqn = E*I*k^4-m*v^2*k^2+2*m*v*w*k+(m+M)*w^2
sol_exact = solve(Eqn, k, 'MaxDegree', 4); %valid for symbolic variables, gives LONG exact solutions
sol_numeric = vpasolve(Eqn, k); %valid only if numeric values are known for everything except k, gives numeric solutions
More Answers (0)
See Also
Categories
Find more on Calculus in Help Center and File Exchange
Community Treasure Hunt
Find the treasures in MATLAB Central and discover how the community can help you!
Start Hunting!