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Unformatted text preview: 10 pts 3. A uniform rod of length L and mass m 1 is attached to a cart of mass m 2 by means of a spring with spring constant k (ﬁgure 3). There is a constant force F that is always applied perpendicular to the free end. The nonlinear equations of motion for this system in terms of the generalized coordinates θ and x are: ¨ L L L θ : I θ + m 1 g sinθ − k cosθ ( x − sinθ ) = FL (7) 2 2 2 L x : m 2 x ¨ + k ( x − sinθ ) = 0 (8) 2 Identify the equilibria and derive the linearized equations for small perturbations about the equilibria (you do not have to solve these equations). Figure 3: Cite as: Thomas Peacock, course materials for 2.003J/1.053J Dynamics and Control I, Spring 2007. MIT OpenCourseWare (http://ocw.mit.edu), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY]....
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- Force, MIT OpenCourseWare, DD Month YYYY, Thomas Peacock, 2.003J/1.053J Dynamics