How to Solve the Initial Condition Problem for Finding A_x and A_y Expressions?

In summary, the conversation discusses the difficulties of solving for A and phi in a given equation involving X, Y, V_x, and initial conditions. The use of either cos(ωt + φ) or Acosωt + Bsinωt is mentioned, with the book preferring the latter method. The conversation also mentions the use of t=0 to solve for phi and the difficulties of using the first method.
  • #1
nhrock3
415
0
i can't see how they got X and Y expressions
V_x is the derivative of X(t) by t
'A' and phi are needed to be found
but when i don't know how to innpur the initial condition to find A_x and A_y
because when we integrate x' expression bot sides i get
x(t)-x(0)=[A_x*cos(wt+phi)]/w - [A_x*cos(0+phi)]/w
so i can't put 'b' instead of x(0) but it doesn't give me A_x parameter value
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  • #2
hi nhrock3! :smile:

(pleeeeeeeeeeease don't post such wide pictures! :redface:)
nhrock3 said:
i can't see how they got X and Y expressions
V_x is the derivative of X(t) by t

(have an omega: ω :smile:)

the general solution can be written either as cos(ωt + φ), or as Acosωt + Bsinωt …

the book uses the second method to get the constants :wink:
 
  • #3
i only used the first
how to do the second?
 
  • #4
uhh? :confused: x(0) = A, x'(0) = ωB
 
  • #5
why uhh? :)
 
  • #6
ahh ok i understand
 
  • #7
why i can't do it the first method
i want to solve it the irst way
 
  • #8
you can solve it the first way, it's just more difficult …

put t = 0 and chug away :smile:​
 
  • #9
i put t=0
and get that phi=0
what next?
 

Related to How to Solve the Initial Condition Problem for Finding A_x and A_y Expressions?

1. What is the initial condition problem?

The initial condition problem is a concept in chaos theory and dynamical systems that refers to the uncertainty in predicting the future behavior of a complex system due to small variations in the initial conditions.

2. Why is the initial condition problem important?

The initial condition problem is important because it highlights the limitations of predictability in complex systems. It shows that even small variations in initial conditions can lead to drastically different outcomes, making it difficult to accurately predict the future behavior of these systems.

3. How does the initial condition problem relate to chaos theory?

The initial condition problem is a fundamental aspect of chaos theory. Chaos theory studies the behavior of complex systems and how small changes in initial conditions can lead to significant changes in the system's behavior over time. The initial condition problem illustrates this sensitivity to initial conditions.

4. Can the initial condition problem be solved?

No, the initial condition problem cannot be solved in most cases. This is because complex systems are highly sensitive to initial conditions and it is impossible to have perfect knowledge of all the initial conditions. However, in some cases, researchers can use techniques such as averaging or controlling initial conditions to reduce the effects of the initial condition problem.

5. How do scientists study the initial condition problem?

Scientists study the initial condition problem through mathematical models and computer simulations. They can also conduct experiments in controlled environments to observe how small changes in initial conditions can affect the behavior of complex systems. Additionally, scientists use statistical methods and data analysis to understand the behavior of complex systems and the role of initial conditions.

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