Derive the differential equation of the two degree-of-freedom model of the machine tool of Chapter Problem 6.8

Question:

Derive the differential equation of the two degree-of-freedom model of the machine tool of Chapter Problem 6.8 using \(x\) and \(\theta\) as generalized coordinates.

Data From Chapter Problem 6..8:

A two degree-of-freedom model of a machine tool is illustrated in Figure P6.8. Using \(x_{1}\) and \(x_{2}\) as generalized coordinates, derive the differential equations governing the motion of the system.

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