6.4 oil can light (low oil pressure)

I have a 2008 6.4. When I do a cold start or start after its sat for a little bit it throws the low oil pressure light. When it does this the truck kinda shakes like a rough idle so too speak. I'm in Ohio and running 15w-40 motorcraft oil and filter. Also the oil cap is ford OEM as well. Any ideas and help would be greatly appreciated.

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