Question
Download Solution PDFWhat is the critical speed of the shaft if its natural frequency of transverse vibration is 2.85 Hz?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept:
The relation between time-period (T), angular velocity (ω) and frequency (f) is given by:
\(T=\frac{2π}{ω}=\frac{1}{f}\)
We know that angular velocity (ω) can be represented in terms of angular speed (N):
\(ω=\frac{2π N}{60}\)
Calculation:
Given:
f = 2.85 Hz
\(T=\frac{2π}{ω}=\frac{1}{f}\)
\(\frac{2π}{ω}=\frac{1}{f}\)
ω = 2πf ⇒ 2π × 2.85 Hz
\(ω=\frac{2π N}{60}\)
\(N=\frac{60}{2\pi}\times \omega\)
\(N=\frac{60}{2\pi}\times 2\pi\;\times2.85=171\;rpm\)
Last updated on May 28, 2025
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