A mass, m, is supported on a light beam, which is free to rotate about the pivot at O as illustrated in the figure below (note figure is not drawn to scale). The beam is supported by two springs of stiffness, k₁ and k2, located at a distance, L and a respectively, from the pivot. Additionally a damper with damping coefficient cis located a distance b from the pivot. A step force of constant magnitude, F(t) = Fo is applied to the mass from time t = 0 as illustrated. Using the data below, derive the equation of motion of the system. m = 15.6kg; a=0.5m; b=0.8m; r = 0.62m; L = 1.25m; k₁ = 772Nm¹;k2 = 340Nm¹; c= 95Ns/m; Fo= 86N Determine the moment of inertia of the system, Io, about point O.

A mass, m, is supported on a light beam, which is free to rotate about the pivot at O as illustrated in the figure below (note figure is not drawn to scale). The beam is supported by two springs of stiffness, k₁ and k2, located at a distance, L and a respectively, from the pivot. Additionally a damper with damping coefficient cis located a distance b from the pivot. A step force of constant magnitude, F(t) = Fo is applied to the mass from time t = 0 as illustrated. Using the data below, derive the equation of motion of the system. m = 15.6kg; a=0.5m; b=0.8m; r = 0.62m; L = 1.25m; k₁ = 772Nm¹;k2 = 340Nm¹; c= 95Ns/m; Fo= 86N Determine the moment of inertia of the system, Io, about point O.

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

A mass, m, is supported on a light beam, which is free to rotate about the pivot at O as
illustrated in the figure below (note figure is not drawn to scale). The beam is supported
by two springs of stiffness, k₁ and k2, located at a distance, L and a respectively, from the
pivot. Additionally a damper with damping coefficient cis located a distance b from the
pivot. A step force of constant magnitude, F(t) = Fo is applied to the mass from time t = 0,
as illustrated. Using the data below, derive the equation of motion of the system.
m = 15.6kg; a = 0.5m; b=0.8m; r = 0.62m; L = 1.25m;
k₁ = 772Nm¹k2 = 340Nm-¹;c = 95Ns/m; Fo= 86N
Determine the moment of inertia of the system, Io, about point O.
Io(kgm2):
If the equation of motion for the system is written in the form +pe+q0 = Po, what are the
values of p, q and Po.?
p.
q
Po
Hence, determine :
The natural frequency of oscillation of the system, wn (rad/s):
The damping ratio, C
r
F(t)
L
퍼
K₁²
Ꮎ

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