All Problems

Mechanical Oscillations

Problem 4.31

In the arrangement shown in Fig. 4.8 the sleeve \(M\) of mass \(m=0.20 \mathrm{~kg}\) is fixed between two identical springs whose combined stiffness is equal to \(x=20 \mathrm{~N} / \mathrm{m} .\) The sleeve can slide without friction over a horizontal bar \(A B .\) The arrangement rotates with a constant angular velocity \(\omega=4.4 \mathrm{rad} / \mathrm{s}\) about a vertical axis passing through the middle of the bar. Find the period of small oscillations of the sleeve. At what values of \(\omega\) will there be no oscillations of the sleeve?

Reveal Answer
T=2π/Vx/m−ω2‾=0.7 s,ω⩾x/m=10rad/sT=2 \pi / V \overline{x / m-\omega^{2}}=0.7 \mathrm{~s}, \omega \geqslant \sqrt{x / m}=10 \mathrm{rad} / \mathrm{s}
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