Whole Lotta Shakin\' An experimental package and its support structure are inten
ID: 1568078 • Letter: W
Question
Whole Lotta Shakin' An experimental package and its support structure are intended to be placed on board the International Space Station. The package and its support structure act as a spring-mass system with a force constant of 2.13×106 N/m and a mass of 105 kg . A NASA requirement for any experimental package, so that the package is not damaged by shaking during launch from Earth's surface, is that resonance for forced oscillations not occur for any frequency below 35 Hz. Part A What is the natural vibrational frequency of this package and support structure? Also, what is the resonant frequency of this package and support structure? natural frequency, resonant frequency =
Explanation / Answer
Given that,
k = 2.13*10^6 N/m
m = 105 kg
angular speed w = sqrt (k / m)
w = sqrt (2.13*10^6 / 105) = 142.42 rad/s
natural frequency f = w / 2*pi
f =142.42 / 2*3.14
f = 22.68 Hz
As given that resonance for forced oscillations do not occur for any frequency below 35 Hz.
given frequency is below 35 Hz. so, resonance will not occur.
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