1. Figure 1 shows a rocking mechanism that consists of two masses m₁ and m₂ connected by a rigid and massless rod, which is pivoted with two unequal arms of lengths a and b. The lower mass m₁ is laterally supported by a viscous damper with damping coefficient c, while the upper mass m₂ is by a linear spring with spring constant k. The damper and the spring are undeformed when the rod is vertical. The rocking angle from the vertical is 0(t) and the horizontal displacement of the upper mass is r(t). A moment Mo(t) is applied to the rod at the pivot. The rocking mechanism is in the vertical plan and g is the gravitational acceleration. Derive the equation of motion governing (t) of the rocking mechanism in Fig. 1. Assume that the motion is small, i.e., 0(t) < 1, so that the spring and damper remain horizontal during the motion. Under the small-motion assumption, how is r(t) related to 0(t)? 18 m₂ X wit m₂ M.(1) Figure 1: A rocking mechanism with two unequal arms

1. Figure 1 shows a rocking mechanism that consists of two masses m₁ and m₂ connected by a rigid and massless rod, which is pivoted with two unequal arms of lengths a and b. The lower mass m₁ is laterally supported by a viscous damper with damping coefficient c, while the upper mass m₂ is by a linear spring with spring constant k. The damper and the spring are undeformed when the rod is vertical. The rocking angle from the vertical is 0(t) and the horizontal displacement of the upper mass is r(t). A moment Mo(t) is applied to the rod at the pivot. The rocking mechanism is in the vertical plan and g is the gravitational acceleration. Derive the equation of motion governing (t) of the rocking mechanism in Fig. 1. Assume that the motion is small, i.e., 0(t) < 1, so that the spring and damper remain horizontal during the motion. Under the small-motion assumption, how is r(t) related to 0(t)? 18 m₂ X wit m₂ M.(1) Figure 1: A rocking mechanism with two unequal arms

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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