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I am sorry to hear this.
The letter is good.
In court you would have to prove that the noise or vibrations are above community standards and are depriving you of your right to peaceful enjoyment of your home. This noise/ vibration is considered a nuisance and is a tort or civil wrong doing just as if they were throwing dirt into your yard, for example.
Does that help?
There is nothing that specifies what community standards are in this case but you would likely need an expert to provide a report.
You should really see a local lawyer and have that lawyer start to write letters threatening a lawsuit.