be convinced that ... = believe that ...在這個(gè)句式中，that從句是陳述語(yǔ)氣，不是虛擬語(yǔ)氣，時(shí)態(tài)受前面be的限制。

你提供的這個(gè)句子，needed 是實(shí)意動(dòng)詞，不是情態(tài)動(dòng)詞（后面跟了to do），是一般過(guò)去時(shí)，跟前面was 的時(shí)態(tài)一致。再舉數(shù)例：I was convinced that he knew the truth. 我確信他知道事實(shí)。They were convinced that he would not fail them. 他們相信他不會(huì)辜負(fù)他們的期望。You will soon be convinced that she is right. 你不久就會(huì)相信她是對(duì)的。You will be convinced that our product is superior. 你一定會(huì)相信我們的產(chǎn)品比別家的好。I am not at all convinced that he's so cool a head. 我根本沒(méi)法相信他的頭腦這么冷靜。I am convinced that she is innocent. 我堅(jiān)信她是清白無(wú)辜的。I'm convinced that what you said is quite right. 我相信你說(shuō)的是對(duì)的。I was convinced that we were doing the right thing. 我堅(jiān)信我們做的事是對(duì)的。He was convinced that his theories were correct. 他確信他的學(xué)說(shuō)是正確的。They were convinced that we should give it a try. 他們認(rèn)為我們應(yīng)該試一下。I felt convinced that he would succeed. 我確信他會(huì)成功。I am convinced that is true. 我肯定那是正確的。