I have a Seagate FreeAgent GoFlex 500Gb Beeps continuously
It does not even gets detected
What could be the cause of that motor spindle or firmware ?

Most likely stiction. Unless it was dropped then MAYBE motor spindle, but i would say 9/10 stiction. Very common. Heads did not park and are stuck to platters.

Requires professional service.

Sometimes if drive isn't getting enough power (USB) you can get some strange symptoms.

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Death is nothing, but to live defeated and inglorious is to die daily.
Data Recovery Cape Town

It dOes Not spin it only beeps

Well champ .
In your Case the Head of the hdd is stuck on the platter .you need to give it to a DR professional so that he can open the hdd in a Clean Room and try and recover your data .In india this kind of Dr would Be Rs :18750/- Only

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Regards
Amarbir S Dhillon , Chandigarh Data Recovery Labs [India]
Logical,Semi Physical And Physical Data Recovery
Website-> http://www.chandigarhdatarecovery.com