Question

a mass of 1kg is suspended form a spring with a shiftness constant of 24N/m. If the undamped frequency is 1.156 times the damped frequency. Calculate the damping factor?

Answer 1

A mass of $1\mathrm{kg}$ is suspended from a spring with a shiftness constant of $24\mathrm{N/m}$. If the undamped frequency is 1.156 times the damped frequency. Calculate the damping factor?

Solution

$$\omega_{\mathrm{d}} = \omega_0 \sqrt{1 - \zeta^2}$$

damping ratio $\zeta = \sqrt{1 - \left(\frac{\omega_d}{\omega_0}\right)^2} = 0.5$

$$\zeta = \frac{c}{2\sqrt{mk}}.$$

the viscous damping coefficient $c = 2\zeta\sqrt{mk} = 2 * 0.5\sqrt{1 \times 24} = 4.9 \, \mathrm{N} \, \mathrm{s/m}$