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

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In summary, the conversation is about determining the time it takes for a flow with a given initial condition to reach a specific value, and discussing the use of an equation involving the velocity of the flow. The differential equation θ'=1-cosθ is also mentioned and the possibility of solving it is brought up.
  • #1
1670frank
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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...
 
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  • #2
1670frank said:
θ'=1-cosθ
By θ' I assume you mean dθ/dt, right? Can you solve that differential equation?
 
  • #3
Yes, you can write it as you say
 
  • #4
I also asked whether you can solve the DE. I don't understand what you mean by "the velocity of θ' "
 

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

What is the equation θ' = 1-cosθ used for in "Solve Flows Homework"?

The equation θ' = 1-cosθ is used to represent the rate of change of a variable, θ, over time. In this specific case, it is used to model the behavior of a flow over time.

How do you solve the flows homework using the equation θ' = 1-cosθ?

To solve the flows homework, you can use the equation θ' = 1-cosθ to find the value of θ at different time intervals. This will give you a better understanding of the behavior of the flow over time.

What is the significance of T(A) in the equation θ' = 1-cosθ?

In the equation θ' = 1-cosθ, T(A) represents the period of the flow. It is the time it takes for the flow to complete one full cycle. This value is important in understanding the behavior of the flow over time.

How do you find T(A) in the flows homework?

To find T(A) in the flows homework, you can use the equation T(A) = 2π/ω, where ω is the angular velocity. In this case, ω is equal to 1 since it is the coefficient of cosθ in the equation θ' = 1-cosθ.

What is the behavior of the flow at A=0 in the flows homework?

At A=0, the flow exhibits a simple harmonic motion. This means that it oscillates back and forth between two points with a constant period and amplitude. The behavior at A=0 can be further understood by analyzing the graph of the flow over time.

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