How to remount a 'My Passport' drive incorrectly ejected?

Have a My Passport Drive that  operated satisfactorily for about 2 years and now contains important data. It was accidently disconected without the proper ejection procedure. Now, it will not mount and does not appear in Disk Utility. When connected to the USB port, the small white light illuminates on the WD suggesting the unit is ready for use, but the iMac cannot recognise it.

A forum search seems to suggest the only way now is to use a data recovery app to extract the wanted data and reformat the drive. Is there not a simpler approach to have the computer accept the WD  drive? Any suggestions in that direction would be appreciuated

If the data if corrupted the easiest way if with a data recovery app, if not you will need the help of a professional data recovery company. 

If the drive is not detected by Disk Utility you may try using an additional cable, and other computer if available.  If issue persists the drive will need to be replaced.