你举的不是病句,可以用the的 e.g.
It is an English book (that / which) I bought yesterday.它是我昨天买的书.(本句是对What is that?问句的回答,that所引导的是定语从句,that可被省略)
It was the English book that I bought yesterday.昨天我所卖的就是这本书.(本句相当于对I bought the English book yesterday中an English book进行强调)
the experiment my father did in the lab yesterday evening此句不是完整的句子,是一个定语从句,“my father……”修饰“the experiment”
the改成an后（an experiment my father did in the lab yesterday evening）,把an experiment放到my father 后就行了.
被强调的是人时两个都可以用e.g.It is my mother that/who cooks every.