There are four samples P, Q, R and S with natural frequencies

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There are four samples P, Q, R and S with natural frequencies 64,96,128 and 256 Hz, respectively. They are mounted on test setups for conducting vibration experiments. If a loud pure note of frequency 144 Hz is produced by some instrument, which of the samples will show the most perceptible induced vibration?

1. P
2. Q
3. R
4. S

Correct Option: C

R produces vibration close to natural frequency 144 Hz.

30. d = 0.9 f_n
⇒ ω_d = 0.9 ω_n
⇒ √ω_n² - α² = 0.9 ω_n
Squaring ω_n² - α² 0.81ω_n²
⇒ 0.19 ω_n² = α²

⇒ 0.19 ×	s	=	c²
	m		(2m)10²

⇒ c² = 0.76 sm
⇒ c = √0.76 × 1 × 10³ × 0.1
= 8.717 Ns/m