# Large Damped Harmonic Oscillator misunderstanding

So I'm confused, here with what is highlighted. When the book says of "order $1/y_-$" you will reduce the displacement by a factor of $1/e$. Does of order mean when the time is equal to $1/y_-$, if that's the case (I've tried it with a few examples) you won't ever get exactly X - (1/e)X for the displacement, it will always be less than that from what I observed. So what do they mean? I feel like I'm overthinking this.

• "Reduced by a factor of $1/e$" doesn't mean "reduced from $X$ to $X - (1/e)X$." It means "reduced from $X$ to $(1/e)X$." Incidentally, the notation is not $y$, it's $\gamma$ (gamma). Sep 8, 2018 at 15:45
• Hi, welcome to Physics SE! Can you convert the picture of the text into typed-out, formatted text? It makes the content index-able by search engines, and shows up better on different devices' displays. For formulae, try MathJax instead.
– user191954
Sep 8, 2018 at 16:15
• I can't I'm in the army doing all this on a phone I have no idea how to type it in with math text Sep 8, 2018 at 16:24

## 1 Answer

Go with your feelings on this one: you are overthinking it.

"On the order of" does not mean "exactly", and "reduced by a factor of $1/e$" means:

$$X\rightarrow X/e \ne X-X/e$$