Discussion
A linear spring-mass-dashpot system with a mass of 2 kg is set in motion with viscous damping. If the natural frequency is 15 Hz, and the amplitudes of two successive cycles measured are 7.75 mm and 7.20 mm, the coefficient of viscous damping (in N.s/m) is
Answer: A
The damping coefficient is 4.41 N.s/m.
From two successive amplitudes, the logarithmic decrement and damping ratio are
\[ \begin{aligned} \delta &= \ln\frac{7.75}{7.20} = 0.0736 \\ \zeta &= \frac{\delta}{\sqrt{4\pi^{2} + \delta^{2}}} = 0.01171 \end{aligned} \]
The natural frequency is \(\omega_{n} = 2\pi \times 15 = 94.25\) rad/s, so
\[ \begin{aligned} c &= 2\zeta m\omega_{n} \\ &= 2 \times 0.01171 \times 2 \times 94.25 = 4.41 \end{aligned} \]
Forgetting to convert 15 Hz to rad/s would give a value about six times too small, and the other options do not follow from the measured amplitudes.
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