How to solve equation with several unknown variables for a specific variable?

Question

Studentguy 2023-12-9

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/2058469-how-to-solve-equation-with-several-unknown-variables-for-a-specific-variable

评论： Star Strider 2023-12-9

采纳的回答： Star Strider

Hello

Im trying to solve an equation using the following code:

syms w0 g l r l a m

eqn = m*g*l*(1-cos(a))==1/2*1/2*m*(r^2+2*l^2)*((r^2/(r^2+2*l^2))*w0)^2

Sa = solve(eqn,cos(a))

However it gives me these answers:

eqn =

logical

0

Warning, solving 2 equations for 1 variables

Sa =

1/2 pi

I know the answer should be:

cos(a)=1-(w0^2/(4*g*l))*(r^4/(r^2+2*l^2))

Is there any way to solve this problem? Any help is greatly appreciated!

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Answer 1

Star Strider 2023-12-9

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https://ww2.mathworks.cn/matlabcentral/answers/2058469-how-to-solve-equation-with-several-unknown-variables-for-a-specific-variable#answer_1368584

在 MATLAB Online 中打开

The isolate function is helpful here —

syms w0 g l r l a m

eqn = m*g*l*(1-cos(a))==1/2*1/2*m*(r^2+2*l^2)*((r^2/(r^2+2*l^2))*w0)^2

eqn =

eqn2 = isolate(eqn,cos(a))

eqn2 =

Sa = rhs(eqn2)

Sa =

Sa = simplify(Sa, 500)

Sa =

.

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Studentguy 2023-12-9

Thanks you so much!

Star Strider 2023-12-9

As always, my pleasure!

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Answer 2

John D'Errico 2023-12-9

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此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/2058469-how-to-solve-equation-with-several-unknown-variables-for-a-specific-variable#answer_1368579

在 MATLAB Online 中打开

When you pose it as you did to solve, solve assumes you are trying to solve TWO equations, one of which is the equation

cos(a) == 0

READ THE WARNING MESSAGE!

Instead, do this:

syms w0 g l r l a m

eqn = m*g*l*(1-cos(a))==1/2*1/2*m*(r^2+2*l^2)*((r^2/(r^2+2*l^2))*w0)^2;

isolate(eqn,cos(a))

ans =

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Studentguy 2023-12-9

Thanks a lot!

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