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Elements Of Electromagnetics
7th Edition
ISBN: 9780190698614
Author: Sadiku, Matthew N. O.
Publisher: Oxford University Press
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![### Problems on Spring-Mass Systems in Equilibrium
**12.**
**[C/G]** A 4 lb weight stretches a spring 1 ft in equilibrium. An external force \( F(t) = 0.25 \sin 8t \) lb is applied to the weight, which is initially displaced 4 inches above equilibrium and given a downward velocity of 1 ft/s. Find and graph its displacement for \( t > 0 \).
**13.**
A 2 lb weight stretches a spring 6 inches in equilibrium. An external force \( F(t) = \sin 8t \) lb is applied to the weight, which is released from rest 2 inches below equilibrium. Find its displacement for \( t > 0 \).
**14.**
A 10 gm mass suspended on a spring moves in simple harmonic motion with a period of 4 s. Find the period of the simple harmonic motion of a 20 gm mass suspended from the same spring.
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### Explanation of Graphs and Diagrams
There are no explicit graphs or diagrams provided. For problems 12 and 13, students might be expected to plot the displacement as a function of time \( t \). The graph would typically show oscillations due to the harmonic nature of the spring system, incorporating the effects of the external force.](https://content.bartleby.com/qna-images/question/f57c5c9b-acb3-4a3d-a39b-55eeff7ee4ad/08388b72-875b-4d48-9b64-c8610bb42ca1/4b3tkkj_thumbnail.jpeg)
Transcribed Image Text:### Problems on Spring-Mass Systems in Equilibrium
**12.**
**[C/G]** A 4 lb weight stretches a spring 1 ft in equilibrium. An external force \( F(t) = 0.25 \sin 8t \) lb is applied to the weight, which is initially displaced 4 inches above equilibrium and given a downward velocity of 1 ft/s. Find and graph its displacement for \( t > 0 \).
**13.**
A 2 lb weight stretches a spring 6 inches in equilibrium. An external force \( F(t) = \sin 8t \) lb is applied to the weight, which is released from rest 2 inches below equilibrium. Find its displacement for \( t > 0 \).
**14.**
A 10 gm mass suspended on a spring moves in simple harmonic motion with a period of 4 s. Find the period of the simple harmonic motion of a 20 gm mass suspended from the same spring.
---
### Explanation of Graphs and Diagrams
There are no explicit graphs or diagrams provided. For problems 12 and 13, students might be expected to plot the displacement as a function of time \( t \). The graph would typically show oscillations due to the harmonic nature of the spring system, incorporating the effects of the external force.
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