From 'Vocabulary' part of The ABC Of Plain Words by Sir E Gowers (1951)

Experience as a verb is the stilted converse of the stilted occasion. The difficulty or inconvenience that X occasions Y experiences.

The Department is at present experiencing an acute shortage of labour.
The difficulties you are experiencing are appreciated by me.
I regret that you are experiencing difficulty with your apparatus.

Experience is well-established as a verb, but it is a stiff one and is used too much in such sentences as those just quoted from official letters. There is no great harm in it in the first example, but the other two are capable of improvement. For instance:

I recognise your difficulties. (Note also the clumsiness of the third person passive.)
I am sorry you are having difficulty with your apparatus.
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