Elements Of Electromagnetics
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.
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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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