Q: How do I sync old shuffle with a new computer? It is asking me if I want to erase my library. I have authorized the computer.

Hello Amy,

Thanks for using Apple Support Communities.

From your post I understand that you're trying to sync your iPod shuffle with a new computer, and you're being prompted that the content on the iPod will be erased.  This means that you have synced your iPod with another iTunes library, and in order to sync it with your new computer, all of the content that is on the iPod shuffle with be erased and replaced with is on your new computer.

You might see a message that your device is synced with another library. This means that you've used a different computer to sync your device in the past, and iTunes can't sync without first erasing and replacing all iTunes content on your device.

Move content from iTunes on your computer to your iPhone, iPad, or iPod touch - Apple Support

To avoid this, you will need to enable the option to Manually manage music in the Summary of your iPod shuffle, and then click on Apply.  So rather than syncing selected playlists, artists, etc, automatically, you will need to drag the content to your iPod from the iTunes library.

Check to make sure that the "Manually manage music and videos" option is turned on:

1. Connect your device to your computer.
2. Open iTunes. Make sure that you have the latest version.
3. Locate and click on your device.
   
4. In the left sidebar, click Summary.
5. Scroll down to the Options section.
6. Click the box next to "Manually manage music and videos."
   
7. Click Apply. 

1. Connect your device to your computer.
2. Open iTunes. Make sure that you have the latest version.
3. Choose the content that you want to add to your device from your iTunes library.
4. Drag the content to your iPhone, iPad, or iPod. A panel should appear. Locate your device.

 

Take care.