The cold water shower tap vibrates at a certain point and then stops when the tap is turned pass this point

I will assume this is an older twist to open stem. The stem is worn and vibrates in tube. Sometimes you can correct by repacking the stem with Teflon rope but it may be easier to just replace the whole stem assembly.

I'm thinking like Brian here, except I think you have "washer chatter" where the washer on the cold stem is worn/torn and causes the noise. Pull the cold water stem and inspect the washer and entire stem assembly and see what you think...;)

Mark