13 ### 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 DiagramsThere 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.

Solution: Given Data: W=2 lbδ=6 inF(t)=sin 8tx(0)=2 indx0dt=0 To Find: Displacement, x(t)

A 2 lb weight stretches a spring 6 inches in equilibrium. An external force F(t) = sin 8t lb is ap- plied to the weight, which is released from rest 2 inches below equilibrium. Find its displacement for t > 0.

A 2 lb weight stretches a spring 6 inches in equilibrium. An external force F(t) = sin 8t lb is ap- plied to the weight, which is released from rest 2 inches below equilibrium. Find its displacement for t > 0.

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

Chemical and Phase Equilibrium

Phase diagrams or equilibrium phase diagrams are the graphical representations that show the phase transformations of the constituting elements with respect to the pressure, temperature, and compositions. The diagrams show the conditions that limit the different phases, namely solid, liquid, and gas. The diagram can also be utilized to verify the relations between the state variables. Most of the phase diagrams are temperature-pressure phase diagrams, with the variable parameter as the composition. Usually other variables such as solubility and pressure parameters are not indicated in the phase diagram. For a one-component system (unary phase diagram), the phase diagram is generally a function of temperature and pressure as the state variables, or temperature and volume. However, for a binary system (two-phase) having two components, the phase diagram is a function of temperature and composition as the state variables only. Coexisting of the different phases of the constituting elements is indicated in the phase diagram. A ternary phase diagram can be characterized by consisting of three phases in equilibrium.

Question

### 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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