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

Thanks

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)]

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

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