When I do the work, I come up with the same answer as choice c. I just want to make sure and double check my work. Thanks! **Problem Statement:**Find the transfer function $\frac{Y(s)}{U(s)}$ from force $u$ to position $y$.**Diagram Explanation:**The diagram shows a mechanical system consisting of two masses, $m_1$ and $m_2$, connected by a spring with spring constant $k$. Mass $m_2$ is subject to an external force $u$. The system is placed on a frictionless surface, allowing the masses to move freely.**Options:**(a) $\frac{m_1 s^2 + k}{m_1 m_2 s^4 + (km_1 + km_1)s^2 + k^2}$(b) $\frac{m_1 s^2 + k}{m_1 m_2 s^4 + (km_1 + km_1)s^2}$(c) $\frac{k}{m_1 m_2 s^4 + (km_1 + km_2)s^2}$(d) $\frac{k}{m_1 m_2 s^4 + (km_1 + km_1)s^2 + k^2}$(e) none of the above**Solution Explanation:**To solve for the transfer function $\frac{Y(s)}{U(s)}$, one must analyze the system's dynamics, derive the equations of motion for the masses, and convert them into the Laplace domain. The correct expression relates the force $u$ to the position $y$ through these equations, considering the spring dynamics and the inertias of both masses involved.

Answered: Find the transfer function from force u…

Engineering

Mechanical Engineering

Find the transfer function from force u to posi- tion y Y

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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Question

When I do the work, I come up with the same answer as choice c. I just want to make sure and double check my work. Thanks!

**Problem Statement:**

Find the transfer function $\frac{Y(s)}{U(s)}$ from force $u$ to position $y$.

**Diagram Explanation:**

The diagram shows a mechanical system consisting of two masses, $m_1$ and $m_2$, connected by a spring with spring constant $k$. Mass $m_2$ is subject to an external force $u$. The system is placed on a frictionless surface, allowing the masses to move freely.

**Options:**

(a) $\frac{m_1 s^2 + k}{m_1 m_2 s^4 + (km_1 + km_1)s^2 + k^2}$

(b) $\frac{m_1 s^2 + k}{m_1 m_2 s^4 + (km_1 + km_1)s^2}$

(c) $\frac{k}{m_1 m_2 s^4 + (km_1 + km_2)s^2}$

(d) $\frac{k}{m_1 m_2 s^4 + (km_1 + km_1)s^2 + k^2}$

(e) none of the above

**Solution Explanation:**

To solve for the transfer function $\frac{Y(s)}{U(s)}$, one must analyze the system's dynamics, derive the equations of motion for the masses, and convert them into the Laplace domain. The correct expression relates the force $u$ to the position $y$ through these equations, considering the spring dynamics and the inertias of both masses involved.

Expert Solution

Step 1: Write the given data and what is to find

Given:

To find:

Transfer function $fraction numerator Y left parenthesis s right parenthesis over denominator U left parenthesis s right parenthesis end fraction$ .

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