Discussion
The static deflection of a single-degree system under a load equal to its weight is 25 mm. Its natural period is nearest to
Answer: A
Correct answer: 0.32 s
Under a load equal to the weight, \( k = mg/\delta \), so the period reduces to a function of the static deflection alone:
\[ T = 2\pi\sqrt{\frac{\delta}{g}} = 2\pi\sqrt{\frac{0.025}{9.81}} \]
\[ = 2\pi \times 0.0505 = 0.317\ \mathrm{s} \]
Mass and stiffness both cancel, which is what makes the relation so useful: a deflection measurement gives the period directly, and it is the basis of Rayleigh's method applied to a self-weight deflected shape.
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