I am not discriminating against cast iron, but the idea that cast iron or steel have better damping properties than other metals is certainly debateable, and in my mind it just aint true. It dosent really matter where you read it. The book is wrong.
And I say this for the same reason that tuning forks are usually made of steel instead of lead. The more malleable a metal is, the more it will damp vibrations. The harder something is, the better it will vibrate - or ring - like a bell.
Which is also why bells are made from bell bronze, one of the hardest nonferrous metals which exists. Otherwise the liberty bell would have been made of lead - maybe wood.
But none fo this really matters as much as the overall design of an object, which is where the objects resonant frequency comes in. It does make a difference. Look at the difficulty of manufacturing a driveshaft. Maybe you have seen a dynamic balancer - without that step many driveshafts would simply snap inexplicably. The same is true of lathes. If the power source is generating an impulse which is a harmonic of the machines natural freq, then the whole machine will start jumping around the shop like a mexican jumping bean. The design is the main factor.
But that dosent address the fact that chineez tools are garbage.