A mass of 1.0 g is attached to the end of a spring with a stiffness of 20 N/m. a. Determine the critical damping coefficient, c (i.e., the coefficient at which the system transitions between overdamped and underdamped conditions). b. A dashpot is chosen with a damping coefficient equal to one fifth of that determined in part a. This system is to be used as part of a high speed switch system in which a driving force opens and shuts a switch at fast speeds. fim m -X(1) F(t) The gap between the two electrodes is 1.0 mm. In order to close the switch, a sinusoidal force is applied equal to: F(t) = (16 mN) cos t An engineer is designing the switch such that the on/off function is as fast as possible. What is the highest driving frequency that will result in closing of the switch?
A mass of 1.0 g is attached to the end of a spring with a stiffness of 20 N/m. a. Determine the critical damping coefficient, c (i.e., the coefficient at which the system transitions between overdamped and underdamped conditions). b. A dashpot is chosen with a damping coefficient equal to one fifth of that determined in part a. This system is to be used as part of a high speed switch system in which a driving force opens and shuts a switch at fast speeds. fim m -X(1) F(t) The gap between the two electrodes is 1.0 mm. In order to close the switch, a sinusoidal force is applied equal to: F(t) = (16 mN) cos t An engineer is designing the switch such that the on/off function is as fast as possible. What is the highest driving frequency that will result in closing of the switch?
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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![### Spring-Mass System Analysis
**Problem Statement:**
A mass of 1.0 g is attached to the end of a spring with a stiffness of 20 N/m.
**Tasks:**
a. **Determine the critical damping coefficient**, \( c \) (i.e., the coefficient at which the system transitions between overdamped and underdamped conditions).
b. A dashpot is chosen with a damping coefficient equal to one-fifth of that determined in part a. This system is to be used as part of a high-speed switch system in which a driving force opens and shuts a switch at fast speeds.
- **Diagram Explanation**:
- The diagram shows a mass-spring-dashpot system denoted by:
- \( m \): Mass
- \( k \): Spring constant
- \( X(t) \): Displacement over time
- \( F(t) \): Applied force
- The spring and dashpot are attached to a mass, which interacts with a surface on the right.
The gap between the two electrodes is 1.0 mm.
In order to close the switch, a sinusoidal force is applied equal to:
\[ F(t) = (16 \text{ mN}) \cos \omega t \]
An engineer is designing the switch such that the on/off function is as fast as possible. What is the highest driving frequency that will result in closing of the switch?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F25fce74d-50ce-4010-8593-c528dce466b9%2F399aa4a4-21a4-4b1a-9397-20782c3935b5%2Ffr8j5m_processed.png&w=3840&q=75)
Transcribed Image Text:### Spring-Mass System Analysis
**Problem Statement:**
A mass of 1.0 g is attached to the end of a spring with a stiffness of 20 N/m.
**Tasks:**
a. **Determine the critical damping coefficient**, \( c \) (i.e., the coefficient at which the system transitions between overdamped and underdamped conditions).
b. A dashpot is chosen with a damping coefficient equal to one-fifth of that determined in part a. This system is to be used as part of a high-speed switch system in which a driving force opens and shuts a switch at fast speeds.
- **Diagram Explanation**:
- The diagram shows a mass-spring-dashpot system denoted by:
- \( m \): Mass
- \( k \): Spring constant
- \( X(t) \): Displacement over time
- \( F(t) \): Applied force
- The spring and dashpot are attached to a mass, which interacts with a surface on the right.
The gap between the two electrodes is 1.0 mm.
In order to close the switch, a sinusoidal force is applied equal to:
\[ F(t) = (16 \text{ mN}) \cos \omega t \]
An engineer is designing the switch such that the on/off function is as fast as possible. What is the highest driving frequency that will result in closing of the switch?
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