A spring mass system consists of a spring with spring constant k and an attached block of mass m is submerged in a liquid that produces a damping force Fr. m = 2 KG K = 36 N/m F₁ = 18 times the velocity of the center of mass of the block. If the mass is initially released from rest 1m below the equilibrium position: Enter your answer in lower case, ex x"+ax'+bx=0 a. "The second degree equation that describe the motion of the center of mass of the attached block is b. The initial conditions are x(0)= c. The Arbitrary Constants that satisfy the IC's are C= the order does not matter" , x'(0)= C= 11
A spring mass system consists of a spring with spring constant k and an attached block of mass m is submerged in a liquid that produces a damping force Fr. m = 2 KG K = 36 N/m F₁ = 18 times the velocity of the center of mass of the block. If the mass is initially released from rest 1m below the equilibrium position: Enter your answer in lower case, ex x"+ax'+bx=0 a. "The second degree equation that describe the motion of the center of mass of the attached block is b. The initial conditions are x(0)= c. The Arbitrary Constants that satisfy the IC's are C= the order does not matter" , x'(0)= C= 11
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![### Spring Mass System with Damping Force
A spring mass system consists of a spring with spring constant \( k \) and an attached block of mass \( m \) is submerged in a liquid that produces a damping force \( F_{r} \).
#### Given:
- \( m = 2 \) KG
- \( K = 36 \) N/m
- \( F_{r} = 18 \) times the velocity of the center of mass of the block.
If the mass is initially released from rest 1 meter below the equilibrium position:
**Enter your answer in lower case, e.g., \( x'' + ax' + bx = 0 \)**
#### Questions:
a. **The second degree equation that describes the motion of the center of mass of the attached block is**
\[ \boxed{\rule{5cm}{0.4pt}} \]
b. **The initial conditions are**
\[ x(0) = \boxed{\rule{3cm}{0.4pt}} \ , \ x'(0) = \boxed{\rule{3cm}{0.4pt}} \]
c. **The Arbitrary Constants that satisfy the IC's are**
\[ C = \boxed{\rule{3cm}{0.4pt}} \ , \ C = \boxed{\rule{3cm}{0.4pt}} \]
*Note: The order does not matter.*](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc59b3e01-f4fe-4ed0-a002-b05c91db4102%2Fe8c5fc08-ba28-4b99-b81d-72b11e3ad60b%2Fwg74sw4_processed.png&w=3840&q=75)
Transcribed Image Text:### Spring Mass System with Damping Force
A spring mass system consists of a spring with spring constant \( k \) and an attached block of mass \( m \) is submerged in a liquid that produces a damping force \( F_{r} \).
#### Given:
- \( m = 2 \) KG
- \( K = 36 \) N/m
- \( F_{r} = 18 \) times the velocity of the center of mass of the block.
If the mass is initially released from rest 1 meter below the equilibrium position:
**Enter your answer in lower case, e.g., \( x'' + ax' + bx = 0 \)**
#### Questions:
a. **The second degree equation that describes the motion of the center of mass of the attached block is**
\[ \boxed{\rule{5cm}{0.4pt}} \]
b. **The initial conditions are**
\[ x(0) = \boxed{\rule{3cm}{0.4pt}} \ , \ x'(0) = \boxed{\rule{3cm}{0.4pt}} \]
c. **The Arbitrary Constants that satisfy the IC's are**
\[ C = \boxed{\rule{3cm}{0.4pt}} \ , \ C = \boxed{\rule{3cm}{0.4pt}} \]
*Note: The order does not matter.*
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