For the given mechanical system below: a) Write the set of differential equations for the mechanical system given below. b) Draw the equivalent Electrical Circuit. K₁ - 1 N/m 0000 Sv₁ - 2 N-s/m v₂(t) K₂-1 N/m 0000 M₁-1 kg ₂1 N-s/m dv₁ ( K. M₁) v₂(t) f(1) M₂-1 kg v3-1 N-s/m
For the given mechanical system below: a) Write the set of differential equations for the mechanical system given below. b) Draw the equivalent Electrical Circuit. K₁ - 1 N/m 0000 Sv₁ - 2 N-s/m v₂(t) K₂-1 N/m 0000 M₁-1 kg ₂1 N-s/m dv₁ ( K. M₁) v₂(t) f(1) M₂-1 kg v3-1 N-s/m
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
Section: Chapter Questions
Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...
Related questions
Question
This is a part of a review I'm studying, NOT a graded assignment, please do not reject. Thank you!
Am I doing this problem right? I would like someone to verify I'm doing this correctly, thank you!
![**Educational Content: Mechanical and Electrical System Analysis**
**Mechanical System Description:**
The mechanical system consists of two masses, \( M_1 \) and \( M_2 \), each weighing 1 kg. They are connected in series with springs \( k_1 \) and \( k_2 \) both having spring constants of 1 N/m. The system is subjected to damping forces \( fv_1 = 2 \, \text{N·s/m} \), \( fv_2 = 1 \, \text{N·s/m} \), and \( fv_3 = 1 \, \text{N·s/m} \). The velocities of the masses are \( v_1(t) \) and \( v_2(t) \). An external force \( f(t) \) is applied to the system.
**a) Differential Equations:**
1. \( f_{v1} = \frac{dv_1}{dt} (k_1, M_1) \)
2. \( f_{v2} = \frac{dv_2}{dt} (k_2, k_1, M_1, M_2) \)
3. \( f_{v3} = \frac{dv_3}{dt} \left( \frac{k_2}{M_2} \right) \)
The expression for the applied force \( f(t) \) is derived as:
\[ f(t) = \frac{dv_1}{dt} - k_1 M_1 + \frac{dv_2}{dt} (k_2, k_1, M_1, M_2) + \frac{dv_3}{dt} \left( \frac{k_1}{M_2} \right) \]
**b) Equivalent Electrical Circuit:**
The equivalent electrical circuit is drawn with the following components:
- An inductor \( M_1 \) representing mass \( M_1 \).
- Two capacitors representing the spring constants and damping.
- A voltage source, \( f(t) = V_{\text{out}} \), replaces the external force.
Note that the component remarked as "A gate, Not a Capacitor" replaces an element in the system.
This representation helps in understanding the analogous relationship between mechanical damped spring-mass systems and RLC circuits in electrical engineering.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fecd9d238-92a1-4a47-af9e-c758e887edd1%2Fc68003df-7cfc-426d-bfa4-3cdb3f86f263%2Fmlhfwjc_processed.png&w=3840&q=75)
Transcribed Image Text:**Educational Content: Mechanical and Electrical System Analysis**
**Mechanical System Description:**
The mechanical system consists of two masses, \( M_1 \) and \( M_2 \), each weighing 1 kg. They are connected in series with springs \( k_1 \) and \( k_2 \) both having spring constants of 1 N/m. The system is subjected to damping forces \( fv_1 = 2 \, \text{N·s/m} \), \( fv_2 = 1 \, \text{N·s/m} \), and \( fv_3 = 1 \, \text{N·s/m} \). The velocities of the masses are \( v_1(t) \) and \( v_2(t) \). An external force \( f(t) \) is applied to the system.
**a) Differential Equations:**
1. \( f_{v1} = \frac{dv_1}{dt} (k_1, M_1) \)
2. \( f_{v2} = \frac{dv_2}{dt} (k_2, k_1, M_1, M_2) \)
3. \( f_{v3} = \frac{dv_3}{dt} \left( \frac{k_2}{M_2} \right) \)
The expression for the applied force \( f(t) \) is derived as:
\[ f(t) = \frac{dv_1}{dt} - k_1 M_1 + \frac{dv_2}{dt} (k_2, k_1, M_1, M_2) + \frac{dv_3}{dt} \left( \frac{k_1}{M_2} \right) \]
**b) Equivalent Electrical Circuit:**
The equivalent electrical circuit is drawn with the following components:
- An inductor \( M_1 \) representing mass \( M_1 \).
- Two capacitors representing the spring constants and damping.
- A voltage source, \( f(t) = V_{\text{out}} \), replaces the external force.
Note that the component remarked as "A gate, Not a Capacitor" replaces an element in the system.
This representation helps in understanding the analogous relationship between mechanical damped spring-mass systems and RLC circuits in electrical engineering.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 4 steps with 35 images
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, electrical-engineering and related others by exploring similar questions and additional content below.Recommended textbooks for you
Introductory Circuit Analysis (13th Edition)
Electrical Engineering
ISBN:
9780133923605
Author:
Robert L. Boylestad
Publisher:
PEARSON
Delmar's Standard Textbook Of Electricity
Electrical Engineering
ISBN:
9781337900348
Author:
Stephen L. Herman
Publisher:
Cengage Learning
Programmable Logic Controllers
Electrical Engineering
ISBN:
9780073373843
Author:
Frank D. Petruzella
Publisher:
McGraw-Hill Education
Introductory Circuit Analysis (13th Edition)
Electrical Engineering
ISBN:
9780133923605
Author:
Robert L. Boylestad
Publisher:
PEARSON
Delmar's Standard Textbook Of Electricity
Electrical Engineering
ISBN:
9781337900348
Author:
Stephen L. Herman
Publisher:
Cengage Learning
Programmable Logic Controllers
Electrical Engineering
ISBN:
9780073373843
Author:
Frank D. Petruzella
Publisher:
McGraw-Hill Education
Fundamentals of Electric Circuits
Electrical Engineering
ISBN:
9780078028229
Author:
Charles K Alexander, Matthew Sadiku
Publisher:
McGraw-Hill Education
Electric Circuits. (11th Edition)
Electrical Engineering
ISBN:
9780134746968
Author:
James W. Nilsson, Susan Riedel
Publisher:
PEARSON
Engineering Electromagnetics
Electrical Engineering
ISBN:
9780078028151
Author:
Hayt, William H. (william Hart), Jr, BUCK, John A.
Publisher:
Mcgraw-hill Education,