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Mechanical Oscillations

Problem 4.73

A mathematical pendulum oscillates in a medium for which the logarithmic damping decrement is equal to λ0=1.50.\lambda_{0}=1.50 . What will be the logarithmic damping decrement if the resistance of the medium increases n=2.00n=2.00 times? How many times has the resistance of the medium to be increased for the oscillations to become impossible?

Reveal Answer
λ=nλ0/1+(1−n2)(λ0/2π)2=3.3,n′=1+(2π/λc)2=4.3times\lambda=n \lambda_{0} / \sqrt{1+\left(1-n^{2}\right)\left(\lambda_{0} / 2 \pi\right)^{2}}=3.3, n^{\prime}=\sqrt{1+\left(2 \pi / \lambda_{c}\right)^{2}}= 4.3 times
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