Solve x=Asin(ct) and y=Bsin(dt) for the period of the system of two equations

In summary, the conversation revolves around finding a period that satisfies two equations simultaneously. The topic is not well-documented on the internet and the person is looking for help. The equations have their own periods and the goal is to find a time that satisfies both equations simultaneously, which can be achieved through the smallest common multiple of the two periods.
  • #1
SSGD
49
4
I have been trying figure out how to solve the the period of the system of the two equations in the system. I have been searching for examples but this specific topic isn't documented on the internet very well or I'm not very good and searching. Any help would be appriciated.
 
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  • #2
Try posting a specific question in the homework section.
 
  • #3
It's not homework. And the above equations are the specific problem.
 
  • #4
It is homework-like. It is unclear what you mean. Two separate systems with their own period? That is a standard textbook question. Do you look for a common period? Then the smallest common multiple (if existing) will be interesting.
 
  • #5
Each equation has its own period. That is not an issue, there is also a sequence of times where both equations simultaneously repeat.

x(t+Tx)=x(t)
y(t+Ty)=y(t)

x(t+Ts)=x(t)
y(t+Ts)=y(t)

I am looks for Ts a time that satisfies both equations simultaneously.
Sorry for the unclear question.
 
  • #6
SSGD said:
I am looks for Ts a time that satisfies both equations simultaneously.
Then you should use different symbols for the periods.

See above: the smallest common multiple (if it exists) will do the job. If it doesn't exist, there is no such period.
 

1. How do I determine the period of the system of two equations?

The period of the system of two equations can be determined by finding the least common multiple of the periods of each individual equation. This can be done by finding the ratio of the coefficients in the equations, c/a and d/b, and taking the reciprocal of the smaller ratio.

2. Can the period of the system of two equations be infinite?

No, the period of the system of two equations cannot be infinite. The period represents the length of time it takes for the system to repeat itself, so it must be a finite value.

3. How does changing the coefficients affect the period of the system of two equations?

Changing the coefficients in the equations will change the ratio c/a and d/b, which will in turn affect the period of the system. A larger ratio will result in a shorter period, while a smaller ratio will result in a longer period.

4. Can the period of the system of two equations be negative?

No, the period of the system of two equations cannot be negative. The period is a measure of time and must be a positive value.

5. What is the significance of the period in the context of the system of two equations?

The period of the system of two equations represents the amount of time it takes for the system to complete one full cycle. It is an important parameter in understanding the behavior and patterns of the system over time.

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