I’ve had a 2TB My Passport for Mac for two years (almost to the day) and without warning or any damage done to it, has failed to mount accompanied by a beeping/buzzing for a few minutes after being plugged in. It sounds less like a mechanical issue and more like an alarm that something has gone wrong, judging by the regularity and the change in pitch. You can hear for yourself in this video:
In the video the light is solid but other times it has blinked as if it were reading/writing. The disk is not recognized in Disk Utility under any circumstances, however its information does appear in the System Report under USB devices.
I am using the stock USB cable, and have tried both USB ports on my Macbook Air. With no other computer available to me at the moment, I also plugged it into a wall outlet to see if the power source was the issue but the buzzing still occurs.
My Mac is running Sierra 10.12.3 beta, but I was able to access the contents of the drive just fine the day before this started, and nothing on the computer had changed in the time since.