What Causes Arms And Legs Tremor?

My 89 year old mother has developed shaking in her legs and arms. She had a brain scan which showed white spots which the doctor said were normal for someone her age. and she feels that she has something more in her brain causing her problems. She has diabetis and trigeminal neuralgia, osteoporosis and other things that I can't remember at the moment. I want to put her mind at rest as she is vey concerned about the tremors.