A machine of mass 100 kg is subjected to an external harmonic force with a frequency of 40 rad/s. The designer decides to mount the machine on an isolator to reduce the force transmitted to the foundation. The isolator can be considered as a combination of stiffness(K) and damper(damping factor $ξ$ ) in parallel. The designer has the following four isolators:
Arrange the isolators in the ascending order of the force transmitted to the foundation.

1 - 3 - 4 - 1

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1 - 3 - 2 - 4

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3 - 1 - 2 - 4

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4 - 3 - 1 - 2

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Solution

The correct option is D $4 - 3 - 1 - 2$
Transmitted force problem:

$\sqrt{\frac{640 \times 10^{3}}{100}} = 80 \Rightarrow \frac{ω}{ω_{n}} = 0.5$

$\sqrt{\frac{22.5 \times 10^{3}}{100}} = 47.434164 r a d / s$

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The correct option is D 4−3−1−2 Transmitted force problem: √640×103100=80⇒ωωn=0.5 √22.5×103100=47.434164 rad/s

The correct option is D $4 - 3 - 1 - 2$
Transmitted force problem:

$\sqrt{\frac{640 \times 10^{3}}{100}} = 80 \Rightarrow \frac{ω}{ω_{n}} = 0.5$

$\sqrt{\frac{22.5 \times 10^{3}}{100}} = 47.434164 r a d / s$