Solve Flows Homework: θ'=1-cosθ, Find T(A) & Behavior at A=0

  • Thread starter Thread starter 1670frank
  • Start date Start date
1670frank
Messages
5
Reaction score
0

Homework Statement



θ'=1-cosθ If we have the flow starting at θ(0)=A, determine the amount of time, T(A), that it takes to reach θ=pi and what is the leading behavior as A approaches 0.


Homework Equations





The Attempt at a Solution


Well, in my book, they give an equation T=2pi/w where w is the velocity of θ'. T means in this equatio the time the flow requires to go a full circle back to the initial point back to 0. Not sure how to use this equation in this case I think they got this equation by saying that θ(t) changes by 2pi meaning the travel distance while in this case the travel distance is pi-A so T=(pi-A)/w but not exactly sure about this. I really need help with this...
 
Physics news on Phys.org
1670frank said:
θ'=1-cosθ
By θ' I assume you mean dθ/dt, right? Can you solve that differential equation?
 
Yes, you can write it as you say
 
I also asked whether you can solve the DE. I don't understand what you mean by "the velocity of θ' "
 
There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
Back
Top