If you are hard on someone, you treat them severely or unkindly. Don't be so hard on him. soft Hard is also an adverb. He said the security forces would continue to crack down hard on the protestors
A problem is hard for a class if everything in the class can be reduced to it (under some notion of reduction) If a problem is in a class and hard for the class, then it's complete for the class Beware; hard and complete are not synonyms!
If someone is hard put to do something or, in British English if they are hard pushed to do something, they have great difficulty doing it. Mr Morton is undoubtedly cleverer than Mr Kirkby, but he will be hard put to match his popularity
If you strike or take hold of something hard, you strike or take hold of it with a lot of force. I kicked a dustbin very hard and broke my toe. Hard is also an adjective. He gave her a hard push which toppled her backwards into an armchair
Tending toward steeliness, but not quite shrill Often the result of a moderate frequency response hump centered around 6kHz, sometimes also caused by small amounts of distortion