What does a quivering cat tail mean?

very excited to see you

Is it normal for a cat’s tail to shake?

In most cases the shaking tail is a sign of negative emotions, but there are exceptions to every rule. In other words, it’s also possible for your cat to be happy or excited when its tail is vibrating. This can occur if you own a dog-like loyal cat and it’s coming to greet you whenever you arrive home.