Consider the second order ordinary differential equation: d²x(t) dt2 dx(t) + 12- dt + 8x(t) = 8u(t) determine the following: a) The transfer function g(s) = x(s)/u(s) b) The natural frequency of oscillation (wn), c) The damping ratio (3), d) The damped frequency of oscillation (wa),

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8th Edition
ISBN:9781305387102
Author:Kreith, Frank; Manglik, Raj M.
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Chapter4: Numerical Analysis Of Heat Conduction
Section: Chapter Questions
Problem 4.6P
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Question 4:
Consider the second order ordinary differential equation:
d²x(t)
dx(t)
+ 12
dt
+ 8x(t) = 8u(t)
dt2
determine the following:
a) The transfer function g(s) = x(s)/u(s)
b) The natural frequency of oscillation (wn),
c) The damping ratio (3),
d) The damped frequency of oscillation (wa),
e) The system gain (K).
f) State the type of system this is
Transcribed Image Text:Question 4: Consider the second order ordinary differential equation: d²x(t) dx(t) + 12 dt + 8x(t) = 8u(t) dt2 determine the following: a) The transfer function g(s) = x(s)/u(s) b) The natural frequency of oscillation (wn), c) The damping ratio (3), d) The damped frequency of oscillation (wa), e) The system gain (K). f) State the type of system this is
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