Structural Dynamics MCQ with answer and solution

Concept

SDOF undamped natural frequency calculation

Formula

f_n = (1 / (2·π)) × √(k / m)

Step-by-step solution

1. Given mass m = 2 kg and stiffness k = 200 N/m. 2. Undamped circular frequency ω_n = √(k / m) = √(200 / 2) = √(100) = 10 rad/s. 3. Cyclic natural frequency in Hertz f_n = ω_n / (2 × π). 4. f_n = 10 / (2 × 3.14159) = 10 / 6.2832 = 1.592 Hz approx 1.6 Hz. Answer: B

Explanation

The circular natural frequency of a single-degree-of-freedom system is ω_n = √(k/m) = √(200/2) = 10 rad/s. Dividing by 2·π converts this to cyclic frequency f_n = 10 / (2×3.1416) = 1.59 Hz, which rounds to 1.6 Hz.

Why the other options are wrong

A) 0.8 Hz results from incorrectly dividing 10 by 4·π. C) 15.9 Hz is off by a factor of 10 from arithmetic error. D) 31.8 Hz is off by a factor of 20.

Shortcut

f = (1 / 2π) × √(k/m) = 10 / 6.28 ≈ 1.6 Hz.

Common mistake

Reporting circular frequency ω = 10 rad/s instead of dividing by 2·π to obtain cyclic frequency in Hz.