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Question Number 209430 by Tawa11 last updated on 09/Jul/24

Answered by mr W last updated on 10/Jul/24

$$1)$$$${\omega }_0=\sqrt{\frac{k}{m}}$$$$\zeta =\frac{c}{2\sqrt{mk}}$$$${\omega }_r={\omega }_0\sqrt{1-2{\zeta }^2}=\sqrt{\frac{k}{m}(1-\frac{c^2}{2mk})}$$$$=\sqrt{\frac{12}{3}\times (1-\frac{8^2}{2\times 3\times 12})}=0.667rad/s$$$$$$$$2)$$$$z_m=\sqrt{c^2+{(\frac{k}{\omega }-m\omega )}^2}$$$$=\sqrt{8^2+{(\frac{12}{15}-3\times 15)}^2}=44.92\mathrm{\Omega }$$

Commented by Tawa11 last updated on 10/Jul/24

$$\mathrm{Thanks}\mathrm{for}\mathrm{your}\mathrm{time}\mathrm{sir}.$$$$\mathrm{I}\mathrm{really}\mathrm{appreciate}.$$

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