Question

The natural frequency of a spring–mass system is 10 rad/s. Which of the following statements is/are CORRECT?

• A. The mass is 100 kg and the stiffness is 1 N/m.
• B. The mass is 1.25 kg and the stiffness is 125 N/m.
• C. The stiffness is 620 N/m and the mass is 6.2 kg.
• D. The stiffness is 62 N/m and the mass is 620 kg.

Hint:

Natural frequency depends only on the ratio \(k/m\). Multiple combinations can satisfy the same \(\omega_n\).

Answer 1

The Correct Option is B, C

Step 1: Formula for natural frequency.
\[ \omega_n = \sqrt{\frac{k}{m}} = 10 \, rad/s \] \[ \frac{k}{m} = 100 \]

Step 2: Check options.
(A) \(k=1, m=100 \Rightarrow k/m=0.01\), not 100 → Wrong. (B) \(k=125, m=1.25 \Rightarrow k/m=100\) → Correct. (C) \(k=620, m=6.2 \Rightarrow k/m=100\) → Correct. (D) \(k=62, m=620 \Rightarrow k/m=0.1\) → Wrong. Final Answer:
\[ \boxed{\text{(B) and (C)}} \]