The governing differential equation of motion of a damped system is given by $\mathrm{m} \frac{\mathrm{d}^{2} \mathrm{x}}{\mathrm{dt}^{2}}+\mathrm{c} \frac{\mathrm{dx}}{\mathrm{dt}}+\mathrm{kx}=0 .$ If $\mathrm{m}=1 \mathrm{~kg}, \mathrm{c}=2 \mathrm{Ns} / \mathrm{m}$ and $\mathrm{k}=2 \mathrm{~N} / \mathrm{m}$ then the frequency of the damped oscillation of this system is______________rad/s

Question ID - 1 :- The governing differential equation of motion of a damped system is given by $\mathrm{m} \frac{\mathrm{d}^{2} \mathrm{x}}{\mathrm{dt}^{2}}+\mathrm{c} \frac{\mathrm{dx}}{\mathrm{dt}}+\mathrm{kx}=0 .$ If $\mathrm{m}=1 \mathrm{~kg}, \mathrm{c}=2 \mathrm{Ns} / \mathrm{m}$ and $\mathrm{k}=2 \mathrm{~N} / \mathrm{m}$ then the frequency of the damped oscillation of this system is______________rad/s

3537

Answer Key : (0.99: 1.01) -

0.99: 1.01

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The two dimensional state of stress in a body is described by the Airy's stress function:
$\phi=5 \frac{\mathrm{x}^{4}}{12}+\frac{\mathrm{x}^{3} \mathrm{y}}{6}+3 \frac{\mathrm{x}^{2} \mathrm{y}^{2}}{2}+7 \frac{\mathrm{xy}^{3}}{6}+\mathrm{E} \frac{\mathrm{y}^{4}}{12} .$ The Airy's stress function will satisfy the equilibrium
and the compatibility requirements if and only if the value of the coefficient $\mathrm{E}$ is______________