Solve Equation for w(t)
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I need to solve the following equation to w(t). I just need the real part solution. w(t) = .....
All other variables are later given in a table so I can calculate different solutions.
I´m not able to solve this in a m.file?
It would be great if someone can help me. please
Thanks a lot
7 Comments
Rik
on 28 Feb 2021
Deleted comments:
Hello, i tried it with the following code:
syms rho_w w(t) p_u d_0 D_0 l h_0 t kappa m_St m_w rho_L c_w A_Q v(t) h_d lambda zeta n
eqn = (rho_w / 2) * w(t)^2 + p_u == (rho_w / 2) * (d_0 / D_0)^4 * w(t)^2 + ((l - h_0) / (l - h_0 + (d_0 / D_0)^2 * w(t) * t))^kappa + (rho_w / (m_St + m_w - rho_w * (pi / 4) * d_0^2 * w(t) * t)) * (rho_w * (pi / 4) * d_0^2 * w(t)^2 - (rho_L / 2) * c_w * A_Q * v(t)^2) * (h_0 + h_d - (d_0 / D_0)^2 * w(t) * t) + (rho_w / 2) * (d_0 / D_0)^4 * w(t)^2 * (lambda * ((h_0 - (d_0 / D_0)^2 * w(t) * t) / D_0) + sum(zeta,i,1,n)) ;
solx = solve(eqn, w(t))
This equation is now to be solved for w (t), but under the condition that v (t) is known.
Answers (1)
Walter Roberson
on 31 Jan 2021
syms rho_w w(t) p_u d_0 D_0 l h_0 t kappa m_St m_w rho_L c_w A_Q v(t) h_d lambda zeta n
syms sum_of_zeta
eqn = (rho_w / 2) * w(t)^2 + p_u == (rho_w / 2) * (d_0 / D_0)^4 * w(t)^2 + ((l - h_0) / (l - h_0 + (d_0 / D_0)^2 * w(t) * t))^kappa + (rho_w / (m_St + m_w - rho_w * (pi / 4) * d_0^2 * w(t) * t)) * (rho_w * (pi / 4) * d_0^2 * w(t)^2 - (rho_L / 2) * c_w * A_Q * v(t)^2) * (h_0 + h_d - (d_0 / D_0)^2 * w(t) * t) + (rho_w / 2) * (d_0 / D_0)^4 * w(t)^2 * (lambda * ((h_0 - (d_0 / D_0)^2 * w(t) * t) / D_0) + sum_of_zeta) ;
syms W V
eqnW = subs(eqn, w(t), W)
solw = solve(eqnW, W)
char(eqnW)
5 Comments
James Tursa
on 6 May 2021
"... always has an even number of real-valued roots ..."
should read
"... always has an even number of complex-valued roots ..."
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