# Changing periods. Very confusing

• samh
In summary: This will demonstrate that g has a period of 2pi and therefore, f has a period of 2L. In summary, the given function f(x) with period 2L can be transformed into g(t) with period 2pi by using the substitution t=pi*x/L. This can be verified by showing that g(t) = g(t+2pi), proving that f has a period of 2L.
samh
This is driving me nuts:

Suppose f(x) has period 2L, that is, f(x+2L)=f(x) for all x. If we let t=pi*x/L, and
g(t) = f(x) = f(L*t/pi)
then, as you can verify, g has period 2pi.

How do you show that that's true?!? How do you prove it? For the life of me I can't see how this holds despite the fact that I've wasted the past two hours working at it. I can't think of a technical explanation for it (a proof) OR an intuitive one... Please help.

It's simple

$$f\left(\frac{Lt}{\pi}+2L\right)=f\left(\frac{L}{\pi}(t+2\pi)\right)=f\left(\frac{L}{\pi}t\right)$$

So you can see very clearly that if you denote by

$$g(t)=f\left(\frac{L}{\pi}t\right)$$

, then g has a period of 2\pi.

Daniel.

samh said:
This is driving me nuts:

How do you show that that's true?!? How do you prove it? For the life of me I can't see how this holds despite the fact that I've wasted the past two hours working at it. I can't think of a technical explanation for it (a proof) OR an intuitive one... Please help.

To prove it just show that g(t) = g(t+2pi) using the definition of g and the properties of f.

## 1. What causes changes in menstrual periods?

Changes in menstrual periods can be caused by hormonal fluctuations, stress, changes in diet or exercise, certain medications, and underlying health conditions.

## 2. Is it normal to have irregular periods?

It is normal for menstrual periods to be irregular during puberty and perimenopause, as well as for the first few years after starting menstruation. However, if irregular periods persist for more than a few years or occur later in life, it could be a sign of a hormonal imbalance or other underlying health issue.

## 3. How can I track my period to better understand changes?

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## 4. Can stress affect menstrual periods?

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## 5. When should I see a doctor about changes in my menstrual periods?

If you experience sudden or significant changes in your menstrual periods, it is important to consult with a healthcare provider. This is especially true if changes persist for more than a few months, are accompanied by severe pain or discomfort, or if you have other symptoms that may indicate an underlying health issue.

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