Here's a great tutorial on LVDTs, courtesy of Macro Sensors. You'll find information on what LVDTs are and how they work, how they're used (and what industries use them), what varieties of LVDT exist, and what kind of support electronics you'll need if you want to use one. It's easy to save and print the primer; it's available in PDF format.
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www.macrosensors.com/ms-lvdt_faq-tutorial.html