GATE 2021 ME (ME1) – Question 35
Consider a single degree of freedom system comprising a mass $M$, supported on a spring and a dashpot as shown in the figure. If the amplitude of the free vibration response reduces from 8 mm to 1.5 mm in 3 cycles, the damping ratio of the system is _____ (round off to three decimal places).
Practise this question in The GATE Grind →
Show answer and explanation
Correct answer: 0.078 to 0.098
Explanation
Logarithmic decrement per cycle is $\delta=\ln(8/1.5)/3=0.557992$. For underdamped motion, $\delta=2\pi\zeta/\sqrt{1-\zeta^2}$.
Solving gives $\zeta=\delta/\sqrt{4\pi^2+\delta^2}=0.0884591$, rounded to **0.088**.