A 10 kg weight is attached to a spring with constant k = 90 kg/m and subjected to an external force F(t) = -640 sin(5t). The weight begins at rest in its equilibrium position. Find its displacement for t > 0, with y(t) measured positive upwards. y(t)
A 10 kg weight is attached to a spring with constant k = 90 kg/m and subjected to an external force F(t) = -640 sin(5t). The weight begins at rest in its equilibrium position. Find its displacement for t > 0, with y(t) measured positive upwards. y(t)
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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![A 10 kg weight is attached to a spring with a constant \( k = 90 \, \text{kg/m} \) and subjected to an external force \( F(t) = -640 \sin(5t) \). The weight begins at rest in its equilibrium position. Find its displacement for \( t > 0 \), with \( y(t) \) measured positive upwards.
\[ y(t) = \underline{\hspace{3cm}} \]
In this problem, you are tasked with finding the displacement \( y(t) \) of a weight attached to a spring. The system is influenced by an external force described by a sinusoidal function. The goal is to determine the displacement at any time \( t > 0 \), where the positive direction is defined as upwards.
To solve this, you would typically set up the differential equation using Hooke's Law and incorporating the external force. The complete solution involves integrating the resulting equation, taking initial conditions into account. The solution, once determined, will describe how the position of the weight varies over time due to the periodic external force applied.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8804931c-d4d2-4898-b133-9e9dc85111d4%2F9ae68152-502f-4d77-8e9b-5681e22b6934%2Feyixl7e_processed.png&w=3840&q=75)
Transcribed Image Text:A 10 kg weight is attached to a spring with a constant \( k = 90 \, \text{kg/m} \) and subjected to an external force \( F(t) = -640 \sin(5t) \). The weight begins at rest in its equilibrium position. Find its displacement for \( t > 0 \), with \( y(t) \) measured positive upwards.
\[ y(t) = \underline{\hspace{3cm}} \]
In this problem, you are tasked with finding the displacement \( y(t) \) of a weight attached to a spring. The system is influenced by an external force described by a sinusoidal function. The goal is to determine the displacement at any time \( t > 0 \), where the positive direction is defined as upwards.
To solve this, you would typically set up the differential equation using Hooke's Law and incorporating the external force. The complete solution involves integrating the resulting equation, taking initial conditions into account. The solution, once determined, will describe how the position of the weight varies over time due to the periodic external force applied.
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