The equation of motion of a weight, m, attached to a spring and a dashpot damping device is 2 y(t) = e| -2 cos 3t –sin 3t 3 where y(t), measured in feet, is the displacement from the equilibrium position of the spring system and is measured in seconds, see Figure 1. Find the initial position and the initial velocity of the weight, m. Give physical interpretations on your answers.

The equation of motion of a weight, m, attached to a spring and a dashpot damping device is 2 y(t) = e| -2 cos 3t –sin 3t 3 where y(t), measured in feet, is the displacement from the equilibrium position of the spring system and is measured in seconds, see Figure 1. Find the initial position and the initial velocity of the weight, m. Give physical interpretations on your answers.

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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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. a) The equation of motion of a weight, m, attached to a spring and a dashpot damping
device is
2
y(t) = e| -2cos 3t –sin 3t
3
where y(t), measured in feet, is the displacement from the equilibrium position of
the spring system and is measured in seconds, see Figure 1. Find the initial
position and the initial velocity of the weight, m. Give physical interpretations on
your answers.
y = 0 (equilibrium position)
m
Figure 1

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