using the same verb twice
In Chinese historic drama like 新三国, I found quite often that people say the same verb twice, like "(我)理解理解", "敬佩敬佩“, as a short response. Is this a common way of speaking in present China as well? I mean, do I sound natural if I speak like this today?

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是的，用这种方法来强调“理解”或者“敬佩”的程度，一般都是单独使用。

A:我这么做，希望你能理解.
B:理解，理解

A：你理解理解我好不好

这并不是古代的用法，老版三国演义会有很多古语，新版三国基本都是普通话的语法，是当代的用法，不过用得比较少，而且有点太正式

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not all the verbs can be used twice to express such a particular meaning.
IT's hard to make a summary, so you have to REMEMBER when you see it on a Chinese Tv programme.
:)

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it's a kind of subjunctive. It's to express some emotion. It's like "could" "would" in english.
for example, ur mom says: 学习久了要多运动运动。
学习久了要运动 is just a normal state.
学习久了要多运动运动 expresses a kind of emotion, which is ur mom's wish.

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It is common nowadays in China. We often hear people say "收拾收拾＂" 打扮打扮＂ ＂整理整理＂＂放松放松＂＂＂凑合凑合＂"运动运动＂ ＂呼吸呼吸新鲜空气＂ etc. there are too much of them.  Moreover, such as " 游游泳＂＂做做操＂＂翻翻书＂＂伸伸胳膊＂＂弹弹琴＂etc. they are endless.