Visit recursively all files in a folder and insert a specific string

[Hannibal2010]

Dear all,

I have the question that:

I have a directory in Linux, call it: test_directory.
This directory has files and sub-directories. (only text files)
Text file CAN contains the specific string, for example, MY_STRING_1
For example, one line in one text file maybe:
MY_STRING_1 abc xyz blah blah //MY_STRING_1 is not single word in one line.

Now, I want to access ALL files in this directory (include sub-directories) and after each MY_STRING_1, add MY_STRING_2 as new line.
For example:

MY_STRING_1 blah blah blah
abc xyz

will become

MY_STRING_1 blah blah blah
MY_STRING_2
abc xyz

Please give me a help. I am using Linux environment

[Salem]

$ cat baz.c
MY_STRING_1 blah blah blah
abc xyz
$ sed -e '/MY_STRING_1/ahello' baz.c
MY_STRING_1 blah blah blah
hello
abc xyz

Now combine that with say 'find' to find all the text files in a directory, and wrap it up with something looking like

mv file tmp
sed ... tmp > file

[Hannibal2010]

Dear Salem,

I tried your guide.

It can displays my expected result into the screen, but nothing happens with the real file

[Hannibal2010]

I think I found it

find ./ -type f | xargs sed -i '/MY_STRING_1/aMY_STRING_2'