Correct

摆动 vs 摇摆 vs 摇晃

/ bǎidòng vs yáobǎi vs y0áohuàng /
Strokes

Definition

摆动, 摇摆 and 摇晃, all are Verb, which means [swing; sway; rock; shake].

Example

摆动 sometimes involves a bigger range in sway and is often applied to concrete things.It can take an object.
In examples, ① ② 摇晃 or 摇摆 can be used instead. 摆动 can not be reduplicated.
1
hěn
píng
不平
  
,
zài
chē
zhōng
suīzhe
随着
chēshēn
车身
bǎidòng
摆动
lai
起来
  

The road was uneven,and she rocked with the cart.

2
Nèn
绿色
de
liǔzhī
柳枝
zài
chénfēng
晨风
zhōng
bǎidòng
摆动
  

The light green willow twigs are swaying in the morning wind.

3
bǎidòng
摆动
shuāngshǒu
双手
  
,
xiàng
sòngxíng
送行
de
rén
gàobié
告别
  

With her hand waving,she said good-bye to the seeing-off people.

摇摆 is applied to concrete things, and also to abstract things such as "stance", "policy",etc.When it takes an object (such as "hand", "head") it implies disagreement.
In example ④ 摇晃 or 摆动 can be used instead.
摇摆 can be reduplicated, but cannot when it has an object ③ can be reduplicated into ……总有些摇摇摆摆.
4
Xiǎogǒu
小狗
yáobǎi
摇摆
zhāo
wěiba
尾巴
  

The little dog wagged its tail.

5
Jiějie
姐姐
xiàng
di
弟弟
yào
huà
画册
  
,
di
弟弟
jìng
yáobǎi
摇摆
zhāo
xiǎoshǒu
小手
  
,
shuō
  

The sister asked her younger brother to give her the picture book,but he waved his little hands saying no.

6
Zhè
wèi
lǐngdǎo
领导
  
,
zài
zhíxíng
执行
shàng
上级
zhèng
政策
shí
  
,
shi
zuǒ
jiùshì
就是
yòu
  
,
zǒng
yǒuxiē
有些
yáobǎi
摇摆
  

When carrying out policies from above the leader was not always implementing them accurately.

摇晃 is usually applied to concrete things; it can be reduplicated, and can take an object.
7
Dēnglóng
灯笼
zài
fēng
zhōng
yáohuàng
摇晃
zhāo
  
,
dēngguāng
灯光
yǐnyǐnyāoyāo
隐隐约约
de
  

The lantern swung and flickered in the wind.

8
Xiǎowáng
小王
yáohuàng
摇晃
zhāo
màozi
帽子
xiàng
chē
wài
sòngháng
送行
de
父母
shuō
zàijiàn
再见
  

Xiao Wang waved his hat to say goodbye to his parents,who were standing outside the train seeing him off.

9
Xiǎochuán
小船
yáoyáohuànghuǎng
摇摇晃晃
de
  
,
yǒudiǎnr  
有点儿
yūn
  

The boat was rocking and he felt a little sick.

摇晃 sometimes means "to wave sth. in one's hand", as in example ⑧ and the following sentences.
In examples ⑩ ⑪ and ⑫ 摆动 or 摇摆 cannot replace 摇晃.
10
Biè
yáohuàng
摇晃
zhuōzi
桌子
  
,
zài
xiě
写字
ne
  

Don't shake the table.I'm writing.

11
Xiǎoshù
小树
gāng
zhǒng
shàng
  
,
zǒng
yáohuàng
摇晃
  
,
jiù
huì
  

The tree was newly planted.It may die if you always shake it.

12
Zhèzhǒng
这种
yào
  
,
yòng
服用
qián
xiān
yào
yáohuàng
摇晃
xià
  

You'd better shake the bottle of medicine before taking.