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A mass of \( 50 \mathrm{kg} \) is suspended from a spring of stiffness \( 10 \mathrm{kN} / \mathrm{m} \). It is set oscillating and it is observed that two successive oscillations have amplitudes of \( 10 \mathrm{mm} \) and \( 1 \mathrm{mm} \) Determine the damping ratio.

1. 0.315
2. 0.328
3. 0.344
4. 0.353

Correct answer: 0.315

Solution

Successive peak amplitudes in a damped oscillator are linked by the logarithmic decrement. With the amplitude ratio known, you can solve for the damping ratio using the standard underdamped formula, which gives ζ ≈ 0.315.

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