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Consider a pulley system shown below. Assume there is no slip between the cord and the pulley. I is the mass moment of inertia of the pulley about its own centroidal axis.    Find the equations of motion in terms of x.  Select all that apply.

Consider a pulley system shown below. Assume there is no slip between the cord and the pulley. I is the mass moment of inertia of the pulley about its own centroidal axis.    Find the equations of motion in terms of x.  Select all that apply.

Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
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Consider a pulley system shown below. Assume there is no slip between the cord and the pulley. I is the mass moment of inertia of the pulley about its own centroidal axis. 

 

Find the equations of motion in terms of x.  Select all that apply.
**Pulley System Analysis** Consider a pulley system shown below. Assume there is no slip between the cord and the pulley. \( I \) is the mass moment of inertia of the pulley about its own centroidal axis. *Diagram Description:* - The diagram illustrates a pulley system where a mass \( m_1 \) is hanging from a pulley with radius \( R \) and mass \( m_2 \) connected to a spring with constant \( k \). The displacement of the mass \( m_1 \) is shown as \( y \), and the displacement of the pulley system is shown as \( x \). **Problem Statement:** Find the equations of motion in terms of \( x \). Select all that apply. **Possible Answers:** 1. \(\left(4m_1 + m_2 + I/R^2\right) \frac{d^2x(t)}{dt^2} + 2kx = 2m_1g + m_2g\) 2. \(\left(4m_1 + I/R^2\right) \frac{d^2x(t)}{dt^2} + kx = 2m_1g + m_2g\) 3. \(\left(m_1 + m_2 + I/R^2\right) \frac{d^2x(t)}{dt^2} + 2kx = -(m_1g + 2m_2g)\) 4. \(\left(4m_1 + m_2 + I/R^2\right) \frac{d^2x(t)}{dt^2} + kx = -(2m_1g + m_2g)\) 5. \(\left(4m_1 + m_2 + I/R^2\right) \frac{d^2x(t)}{dt^2} + 4kx = m_1g + 2m_2g\) 6. \(\left(4m_1 + m_2 + I/R^2\right) \frac{d^2x(t)}{dt^2} + kx = 2m_1g + m_2g\) ✅ The correct answer is highlighted with a check mark.
Transcribed Image Text:**Pulley System Analysis** Consider a pulley system shown below. Assume there is no slip between the cord and the pulley. \( I \) is the mass moment of inertia of the pulley about its own centroidal axis. *Diagram Description:* - The diagram illustrates a pulley system where a mass \( m_1 \) is hanging from a pulley with radius \( R \) and mass \( m_2 \) connected to a spring with constant \( k \). The displacement of the mass \( m_1 \) is shown as \( y \), and the displacement of the pulley system is shown as \( x \). **Problem Statement:** Find the equations of motion in terms of \( x \). Select all that apply. **Possible Answers:** 1. \(\left(4m_1 + m_2 + I/R^2\right) \frac{d^2x(t)}{dt^2} + 2kx = 2m_1g + m_2g\) 2. \(\left(4m_1 + I/R^2\right) \frac{d^2x(t)}{dt^2} + kx = 2m_1g + m_2g\) 3. \(\left(m_1 + m_2 + I/R^2\right) \frac{d^2x(t)}{dt^2} + 2kx = -(m_1g + 2m_2g)\) 4. \(\left(4m_1 + m_2 + I/R^2\right) \frac{d^2x(t)}{dt^2} + kx = -(2m_1g + m_2g)\) 5. \(\left(4m_1 + m_2 + I/R^2\right) \frac{d^2x(t)}{dt^2} + 4kx = m_1g + 2m_2g\) 6. \(\left(4m_1 + m_2 + I/R^2\right) \frac{d^2x(t)}{dt^2} + kx = 2m_1g + m_2g\) ✅ The correct answer is highlighted with a check mark.
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