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
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Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
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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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