@Alfred_F 
Narrow down the range of analytical solutions and then solve them in turn? That sounds pretty good,

@Alfred_F 

Yes, you are quite right that the background is indeed to solve a similar frequency and mode problem between flexible three-link

@dharr 
This is to solve the frequency of a vibration system. Although the complex solution is also part of the frequency solution, it will not be considered. Thank you very much for your reply.

@Rouben Rostamian  
Thank you for your answer, I didn't think of using the form of graph combination to solve, thank you very much, and found that the solution of fsolve is much faster than analytic

@acer  This equation should have several non-trivial solutions, but I'm not sure about the initial range

@dharr  Ok, I'm going to try it out

@acer 

I used maple to compute the solution of a polynomial equation, which takes a long time and is slow to draw graphs, using the odeplot command at that time

@dharr I've solved it in a different way, I've removed one of the variables, I've got a new solution, I don't know how to solve it, or is there something wrong with my equation.

question11.mw

@dharr 

Why doesn't solve make sense? I was hopeful when I faced this result, but is there no nontrivial solution to this equation? Can we get rid of the trigonometric function and then solve it?

@mmcdara 

I thought that fsolve could give all numerical solutions before, but I did not think that fsolve could only give one. Later, I obtained many results after using solve, including the desired solution. Thank you for your guidance.

@Scot Gould 

I can't solve a couple after I wrap it in []

@acer 

First of all, thank you very much for your very organized reply. At first, I thought Rootof could give roots of all ranges, but I didn't realize that roots between 0.96-1 were not in this range.
Secondly, the solution of this root is really out of order, and my understanding of the solution of the root is wrong.
Finally, what if you want to draw an image that uses Rootof to solve for the maximum root and the second positive root by 3 times?
fuxian2.mw

@acer 

In this program you wrote, the index is used for indexing, but the order of his index is from small to large, so that it can not guarantee that the solution is the corresponding root of the formula - the middle is broken, and the two images on both sides are respectively corresponding to which one?

@acer 

This method has opened up a new way for me. I used to think that solving the function value can better draw the image, but I did not expect the rootof method to be so useful.But why does the middle section have no root? Is it because you can't get it?

@dharr 

Thank you, I have since tried some direct dsolve solutions with the same results as convertsys.And then I'm going to go straight to dsolve.