The Nikon D3000 does not have a focusing motor built-in, relying on the lens to have a motor. The Tamron AF 55-200mm does not have the necessary motor; it only auto-focuses with Nikon cameras that have the motor in the camera body.
For Nikon lenses, you need lenses designated AF-S. For Tamron, you need lenses designated USD and/or BIM.
That probably wasn't the answer you wanted to see, but there it is.
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