The system is now modified, with different values of spring stiffness and damping coefficient applied, and with the same force applied to the mass, the equation of motion now becomes: € + 560 +2550 = 18.9 Initially, when the force is applied, the mass is in the equilibrium position but the beam is rotating in the positive direction, moving with a velocity of 23rad/s. Assuming that the displacement of the beam is small, derive an expression for the torsional response of the beam and mass with time, 0(t). What is the steady state displacement of the system, ss (rad): Determine the time at which the peak displacement occurs, tp and the value of the maximum displacement, peak tp (seconds): epeak(rad):

The system is now modified, with different values of spring stiffness and damping coefficient applied, and with the same force applied to the mass, the equation of motion now becomes: € + 560 +2550 = 18.9 Initially, when the force is applied, the mass is in the equilibrium position but the beam is rotating in the positive direction, moving with a velocity of 23rad/s. Assuming that the displacement of the beam is small, derive an expression for the torsional response of the beam and mass with time, 0(t). What is the steady state displacement of the system, ss (rad): Determine the time at which the peak displacement occurs, tp and the value of the maximum displacement, peak tp (seconds): epeak(rad):

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

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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

b
F(t)
K₂
L
с
k₁.
プ
The system is now modified, with different values of spring stiffness and damping
coefficient applied, and with the same force applied to the mass, the equation of motion
now becomes:
+560 +2550 = 18.9
Initially, when the force is applied, the mass is in the equilibrium position but the beam is
rotating in the positive direction, moving with a velocity of 23rad/s. Assuming that the
displacement of the beam is small, derive an expression for the torsional response of the
beam and mass with time, 0(t).
What is the steady state displacement of the system, 0$$ (rad):
Determine the time at which the peak displacement occurs, tp and the value of the maximum
displacement, peak
tp (seconds):
Opeak(rad):

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 = 772Nm-¹;k2₂ = 340Nm ¹1; c= 95Ns/m; F = 86N

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