2/213 Determine the relationship which governs the ve- locities of the four cylinders. Express all velocities as positive down. How many degrees of freedom are there? Ans. 4vA + 80B + 4vc + UD = 0 3 degrees of freedom D

What is inertia tensor?

Question 5: Consider the mechanical system shown on the next page. Note that this figure contains geometric information. A uniform, homogeneous, slender rod with length L [m] and mass m [kg] can rotate about fixed point O. Its orientation is given by angle (t) [rad], which is defined positive in counterclockwise direction. An external force F(t) [N] acts on the end of the slender rod under a fixed angle of Ø [rad] with the horizontal. The slender rod is connected to a spring with stiffness k [N/m] and unstretched length lo [m] and a damper with damping constant d [Ns/m]. Note that the force exerted by the spring and damper is always directed horizontally. The gravitational acceleration g [m/s2] acts in negative vertical direction. Derive the equation of motion by using a) Newton's second law b) Lagrange's method c) Compare your results (is your answer correct?) d) Determine the equilibrium point when F(t) is zero e) Calculate the mass, stiffness and damping matrix. You don't have to…