All Problems

Mechanical Oscillations

Problem 4.72

There are two damped oscillations with the following periods TT and damping coefficients β:T1=0.10 ms,β1=100 s−1\beta: T_{1}=0.10 \mathrm{~ms}, \beta_{1}=100 \mathrm{~s}^{-1} and T2=10 ms,β2=10 s−1.T_{2}=10 \mathrm{~ms}, \beta_{2}=10 \mathrm{~s}^{-1} . Which of them decays faster?

Reveal Answer
extTheanswerdependsonwhatismeantbythegivenquestion.Thefirstoscillationattenuatesfasterintime.Butifonetakesthenaturaltimescale,theperiodT,foreachoscillation,thesecondoscillationattenuatesfasterduringthatperiod. ext {The answer depends on what is meant by the given ques tion. The first oscillation attenuates faster in time. But if one takes the natural time scale, the period T, for each oscillation, the second oscillation attenuates faster during that period.}
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