### 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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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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