5. A mechanical oscillator with a quality factor of 2 comprises a mass of 50 g attached to a spring of stiffness 3250 N/m. When the mass is subject to an oscillating driving force of magnitude 20 N, the resultant frequency of oscillation of the system is 50 Hz. a). Calculate the value of the mechanical resistance, Rm, for the system. b). What percentage of the maximum power is dissipated in the system when is it driven to oscillate at 50 Hz? c). State whether the system is underdamped, critically damped or overdamped when the driving force is turned off and justify your answer.
5. A mechanical oscillator with a quality factor of 2 comprises a mass of 50 g attached to a spring of stiffness 3250 N/m. When the mass is subject to an oscillating driving force of magnitude 20 N, the resultant frequency of oscillation of the system is 50 Hz. a). Calculate the value of the mechanical resistance, Rm, for the system. b). What percentage of the maximum power is dissipated in the system when is it driven to oscillate at 50 Hz? c). State whether the system is underdamped, critically damped or overdamped when the driving force is turned off and justify your answer.
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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How did they get these answers for b) and c) ?
Transcribed Image Text:5. A mechanical oscillator with a quality factor of 2 comprises a mass of 50 g attached
to a spring of stiffness 3250 N/m. When the mass is subject to an oscillating driving
force of magnitude 20 N, the resultant frequency of oscillation of the system is 50 Hz.
a). Calculate the value of the mechanical resistance, Rm, for the system.
b). What percentage of the maximum power is dissipated in the system when is it
driven to oscillate at 50 Hz?
c). State whether the system is underdamped, critically damped or overdamped when
the driving force is turned off and justify your answer.
Transcribed Image Text:27
b) Xm
So
@ 50 Hz:
=
m = mw -
% of
Por (@son₂)
71
3230
0.05
Elu
"(
M
-
=
5.4 sm
6.4
2x 0.05)
(0.05 X20X 50)
3250
2π X 50.
-1
20² x64
2 x ( 54²³ X64)
Por @ SOH₂ =
-|~
لیا 18.4
31.4
58.62
c) W₁ = (W² - p² ) ²³ = (2-6)
В
({
-
18.4
X100
M
247 vad/s
=
Wd is real I non
imaginary underdampil
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