I get up as soon as the alarm rings. 
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A car alarm went off in the middle of the night (= started ringing). ☊ alarm ☊
An alarm bell went off. ☊ bell ☊
In case of fire, ring the alarm bell. ☊ in case of sth ☊
Set the alarm for 7 o'clock. ☊ set ☊
Opening this door will set off the alarm. ☊ set sth off ☊