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.

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Concept explainers

Free Damped Vibrations

Free vibration is a type of vibration in which the external force is removed after giving the initial displacement to a body/system. In other words, in this type of vibration, force is applied at the initial displacement of the system, and after the initial displacement, force is removed, and the system vibrates at the natural frequency.

Question

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)?
C m₂
الشيخ
m₂
Mo(t)
Figure 1: A rocking mechanism with two
unequal arms

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