GATE ME 2022 Set 2 — Question 31
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Theory of Machines & Vibrations → Free Vibration → Logarithmic Decrement & Damping Ratio
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Question
For a dynamical system governed by the equation,the damping ratio is equal to . The displacement of this system is measured during a hammer test. A displacement peak in the positive displacement direction is measured to be mm. Neglecting higher powers () of the damping ratio, the displacement at the next peak in the positive direction will be ___________ mm (in integer).
Correct answer
1.95 to 2.05
Solution
The logarithmic decrement is defined as the natural logarithm of the ratio of any two successive amplitudes in the same direction:Given that . Since we are told to neglect higher powers of , we can approximate as:Therefore,Given the current peak mm, the next peak is:
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