Question

A diver of mass 100 kg is standing at the tip of a spring board of negligible mass. The natural frequency of the spring board with the diver is 1.6 Hz. What is the static deflection at the tip of the spring board when the diver is standing at the tip?
1. 0.1 mm
2. 981 mm
3. 98.1 mm
4. 9.81 mm

Answer 1

Correct Answer - Option 3 : 98.1 mm

Concept:

Natural frequency is given by

\({{w}_{n}}=\sqrt{\frac{g}{\text{ }\!\!\Delta\!\!\text{ }}}\)

Δ = static mass deflection

Calculation:

Given, ω_n = 1.6 Hz

ωn = 1.6 × 2 π

ωn = 3.2 × π

\({{w}_{n}}=\sqrt{\frac{g}{\text{ }\!\!\Delta\!\!\text{ }}}\)

\(3.2\times \pi =\sqrt{\frac{9.81}{\text{ }\!\!\Delta\!\!\text{ }}}\)

⇒ Δ = 98.1 mm