Is the sum of two periodic functions still periodic? | Summary and Q&A

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February 19, 2018
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blackpenredpen
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Is the sum of two periodic functions still periodic?

TL;DR

The sum of two periodic functions is not always periodic; a counter example is provided.

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Questions & Answers

Q: Is the sum of two periodic functions always periodic?

No, the sum of two periodic functions is not always periodic. A counter example is provided where one function has a period of 2π and the other has a period of π, resulting in a non-periodic sum.

Q: How do you determine the period of a periodic function?

To determine the period of a periodic function, divide 2π by the coefficient of T in the function. This gives the length of one period.

Q: Can you find a period for the sum of two periodic functions when it is periodic?

Yes, it is possible to find the period of the sum of two periodic functions when their sum is periodic. By finding integers that satisfy a certain equation, the smallest positive integer multiplied by the first period gives the period of the sum.

Q: How does finding the least common multiple relate to finding when two runners will meet?

Finding the least common multiple is similar to finding the time at which two runners will meet. By using the least common multiple of their individual times, it gives the time after which they will meet at the same point again.

Summary & Key Takeaways

  • The sum of two periodic functions is not always periodic, despite the periods of the individual functions.

  • Using a counter example, it is shown that if one function has a period with a multiple of π and the other function does not, their sum will not be periodic.

  • However, a method is provided to find the period of the sum of two periodic functions when it is periodic.

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