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to Become....... أصبح , أضحى , ظل , أمسى , بات

The difference between them is "Time"
Each and everyone layout a different time

أصبح = for early morning
أضحى = after 10 o'clock a.m.
ظل = continues "never stop, all the time"
أمسى = for the night "usually after sunset"
بات = sleeping on it "like: he slept happily; translation بات سعيداً"

We "Native Arabic Speakers" usually use أصبح - أمسى - ظل but sometimes you could see بات in stories and novels.

first you must know what are they!
they are "fi3l madhi nakis" "incomplete past verbs"
they are us use: with nominal sentences, they put the sentences in the past, and keep the meaning of state or information
nominal sentences are "sentences without verb and give an information, it doesn't contain actions (there are rules for exceptions)

for the influence: the 2d name (el-kahbar-the information-) will have "fat7a" and not "dhama"
you must know some thing about "djoumla ismia"

for the meaning thanks for RANA, for the use if you need more informations ask plz