When a cats tail vibrates or shakes, it can mean different things depending on the situation and the cats surroundings. Here are some possible meanings:

• Annoyance: If the cats tail is quivering so rapidly that it appears to be vibrating, that often means annoyance, especially if you notice her doing this quickly and out of the blue.
• Anger: When a cats tail seems to be whipping and shaking in a more aggressive and exaggerated manner, that can be a sign that shes angry about something.
• Excitement: If the cats tail is facing upwards or is slightly bent at the tip while shaking or vibrating, it can be a sign of excitement and happiness. For example, a quivering tail can mean that your cat is very excited to see you.
• Frustration or impatience: If you observe just the upper portion of your pets tail shaking, that could mean shes frustrated, restless or impatient about something.
• Scent marking: Sometimes, a cats tail and back muscles quiver as a response to scent marking behavior, where shes tagging her surroundings as "hers".

Its important to look at the cats other body language to find out exactly how she may be feeling. For example, a trashing tail could convey intense interest, ecstasy, or anger depending on the situation.