A spring-mass system executes damped harmonic | vedclass

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(D) The angular frequency of damped oscillations is given by $\omega' = \sqrt{\frac{K}{m} - \frac{b^2}{4m^2}}$.Given $T = \frac{\pi}{12} \ s$,the angu

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$28$

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(D) The angular frequency of damped oscillations is given by $\omega' = \sqrt{\frac{K}{m} - \frac{b^2}{4m^2}}$.Given $T = \frac{\pi}{12} \ s$,the angular frequency is $\omega' = \frac{2\pi}{T} = \frac{2\pi}{\pi/12} = 24 \ rad/s$.Substitute the values $K = 1250 \ N/m$,$m = 2 \ kg$,and $\omega' = 24 \ rad/s$ into the equation:$24 = \sqrt{\frac{1250}{2} - \frac{b^2}{4(2^2)}}$$24 = \sqrt{625 - \frac{b^2}{16}}$Squaring both sides:$576 = 625 - \frac{b^2}{16}$$\frac{b^2}{16} = 625 - 576 = 49$$b^2 = 49 	imes 16 = 784$$b = \sqrt{784} = 28 \ kg/s$.

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