All Problems

Mechanical Oscillations

Problem 4.76

A particle was displaced from the equilibrium position by a distance l=1.0 cml=1.0 \mathrm{~cm} and then left alone. What is the distance that the particle covers in the process of oscillations till the complete stop, if the logarithmic damping decrement is equal to λ=0.020?\lambda=0.020 ?

Reveal Answer
s≈l(1+e−λ/2)/(1−e−λ/2)=2 ms \approx l\left(1+\mathrm{e}^{-\lambda / 2}\right) /\left(1-\mathrm{e}^{-\lambda / 2}\right)=2 \mathrm{~m}
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