GATE 2025 ME – Question 35
A block of mass 1 kg connected to a spring of stiffness 10 N m$^{-1}$ is operating in a viscous medium such that the damping ratio (or damping factor) is equal to the ratio of the damped frequency to the natural frequency. The magnitude of the damping ratio for this system is ________ (rounded off to 2 decimal places).
Practise this question in The GATE Grind →
Show answer and explanation
Correct answer: 0.70 to 0.72
Explanation
The damped frequency is $\omega_d = \omega_n\sqrt{1 - \zeta^2}$, so the ratio $\frac{\omega_d}{\omega_n} = \sqrt{1 - \zeta^2}$. Setting $\zeta = \sqrt{1 - \zeta^2}$ gives $\zeta^2 = \frac{1}{2}$, so $\zeta = 0.71$.