GATE ME 2026 Set 1 — Question 18
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Theory of Machines & Vibrations → Free Vibration → Logarithmic Decrement & Damping Ratio
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Question
In a single degree of freedom vibrating system with only viscous damping, the critical damping coefficient is 350 N s/m and the damping coefficient is 35 N s/m.The logarithmic decrement of the vibrating system is
Correct answer
(A) 0.63
Solution
The critical damping coefficient is given as N s/m.
The damping coefficient is given as N s/m.The damping ratio () is defined as the ratio of the damping coefficient to the critical damping coefficient.Since , the system is underdamped.The logarithmic decrement () for an underdamped system is given by the formula:Substituting the value of :Rounding to two decimal places, the logarithmic decrement is 0.63.Therefore, the correct option is (A).
The damping coefficient is given as N s/m.The damping ratio () is defined as the ratio of the damping coefficient to the critical damping coefficient.Since , the system is underdamped.The logarithmic decrement () for an underdamped system is given by the formula:Substituting the value of :Rounding to two decimal places, the logarithmic decrement is 0.63.Therefore, the correct option is (A).
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