The verb 'Shodan" in Farsi means 'to become' but you should know that it is an auxiliary verb with which you can turn an active verb into the passive one. ie. I broke the window من پنجره را شکستم ------The window was broken = پنجره شکسته شد.
we need 'ast' after 'Shode' and 'Kardeh' in formal writing or speaking not in conversational just in third-person singular forms.