Hello, how to solve this equation EIk^4-mv^2k^2+2mvwk+(m+M)w^2=0 numerically where w is variable,

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shoaib Shoaib 2019-12-10

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https://ww2.mathworks.cn/matlabcentral/answers/495822-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-var

评论： shoaib Shoaib 2019-12-12

采纳的回答： Star Strider

can we solve this for k numerically, sorry this is fourth order equation not two order

Thanks

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Star Strider 2019-12-10

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https://ww2.mathworks.cn/matlabcentral/answers/495822-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-var#answer_405670

编辑：Star Strider 2019-12-10

在 MATLAB Online 中打开

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)]

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Walter Roberson 2019-12-12

在 MATLAB Online 中打开

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