Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN: 9780190698614
Author: Sadiku, Matthew N. O.
Publisher: Oxford University Press
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Free Damped Vibrations
Free vibration is a type of vibration in which the external force is removed after giving the initial displacement to a body/system. In other words, in this type of vibration, force is applied at the initial displacement of the system, and after the init…
Question
### 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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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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Step 3: Find the forcing frequency
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