duly
adverb uk/ˈdʒuː.li/ us/ˈduː.li/
恰当地；适时地；应当地
in the correct way or at the correct time; as expected
He knew he had been wrong, and duly apologized. 他知道自己弄错了，于是便道了歉。
She asked for his autograph and he duly obliged by signing her programme. 她要他的签名，他很爽快地答应了并在她的节目单上签上了自己的名字。