Serway & Jewett — Oscillatory Motion: Problem 44

Why is the following situation impossible? Your job involves building very small damped oscillators. One of your designs involves a spring–object oscillator with a spring of force constant \(k = 10.0 \text{ N/m}\) and an object of mass \(m = 1.00 \text{ g}\). Your design objective is that the oscillator undergo many oscillations as its amplitude falls to 25.0% of its initial value in a certain time interval. Measurements on your latest design show that the amplitude falls to the 25.0% value in 23.1 ms. This time interval is too long for what is needed in your project. To shorten the time interval, you double the damping constant \(b\) for the oscillator. This doubling allows you to reach your design objective.