GATE Papers >> Civil >> 2019 >> Question No 13

Question No. 13 Civil | GATE 2019

A simple mass-spring oscillatory system consists of a mass m, suspended from a spring of stiffness k. Considering z as the displacement of the system at any time t, the equation of motion for the free vibration of the system is $m\overset{\mathit¨}{\mathit z}+kz=0$ . The natural frequency of the system is

Answer : (B) $ \sqrt{\frac km} $

Solution of Question No 13 of GATE 2019 Civil Paper

$ \begin{array}{l}\mathrm m.\ddot{\mathrm z}+\mathrm{kz}=0\\\ddot{\mathrm z}+\frac{\mathrm k}{\mathrm m}.\mathrm z=0\\\\\mathrm{Comparing}\;\mathrm{with}\;\dot{\mathrm x}+\mathrm\omega_{\mathrm n}^2\mathrm x=0\Rightarrow\mathrm\omega_{\mathrm n}^2=\frac{\mathrm k}{\mathrm m}\\\mathrm{Natural}\;\mathrm{frequency},\;\left({\mathrm\omega}_{\mathrm n}\right)=\sqrt{\frac{\mathrm k}{\mathrm m}}\end{array} $

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