If your going to Copenhagen, take the Metro and not the train. They cost the same and take the same amount of time, but the Metro runs every 4th or 6th minute depending upon the time of the day. In addition the is better to take the Metro and get of at Kongen's Nytorv than taking the train and get of at Hovedbanegården. One idea couold be to take the Metro obe way and the train the other way.