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Question 3 (a) A system is critically damped. Derive an expression for the time at which the dispacement achieves a maximum or minimum. What is the time that maximum displacement amplitude occurs for the following: For an aircraft landing, the natural frequency can be taken as 2.5 rad/s, initial displacement is 0 mm and sink rate, i.e. initial velocity is -50mm/s. For the result, roughy sketch the response of the system for the initial conditions.

Question 3 (a) A system is critically damped. Derive an expression for the time at which the dispacement achieves a maximum or minimum. What is the time that maximum displacement amplitude occurs for the following: For an aircraft landing, the natural frequency can be taken as 2.5 rad/s, initial displacement is 0 mm and sink rate, i.e. initial velocity is -50mm/s. For the result, roughy sketch the response of the system for the initial conditions.

Elements Of Electromagnetics
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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Question 3 (a) A system is critically damped. Derive an expression for the time at which the dispacement achieves a maximum or minimum. What is the time that maximum displacement amplitude occurs for the following: For an aircraft landing, the natural frequency can be taken as 2.5 rad/s, initial displacement is 0 mm and sink rate, i.e. initial velocity is -50mm/s. For the result, roughy sketch the response of the system for the initial conditions. (b) The seat of a helicopter with a pilot weighs 1000N and is found to have a static deflection of 10mm under self-weight. The vibration of the rotor is transmitted to the base of the seat as harmonic motion with a frequency of 4Hz and an amplitude of 0.2mm. What are the levels of vibration felt by the pilot including velocity and acceleration?
Transcribed Image Text:Question 3 (a) A system is critically damped. Derive an expression for the time at which the dispacement achieves a maximum or minimum. What is the time that maximum displacement amplitude occurs for the following: For an aircraft landing, the natural frequency can be taken as 2.5 rad/s, initial displacement is 0 mm and sink rate, i.e. initial velocity is -50mm/s. For the result, roughy sketch the response of the system for the initial conditions. (b) The seat of a helicopter with a pilot weighs 1000N and is found to have a static deflection of 10mm under self-weight. The vibration of the rotor is transmitted to the base of the seat as harmonic motion with a frequency of 4Hz and an amplitude of 0.2mm. What are the levels of vibration felt by the pilot including velocity and acceleration?
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