The figure shows a system of two equal masses m and three massless horizontal
springs with spring constants k1 , k2 , k1. Ignore gravity. The masses can move only
in the horizontal direction and there is no dissipation. If m = 1, k1 = 2 and k2 = 3
(all in appropriate units), the frequencies of the normal modes of the system in the
same system of units are
Options:
(A) √2 , √8
(B) √2 , √6
(C) √3 , √10
(D) √3 , √8
Official Answer Key:
B
Step-by-Step Solution & Explanation
### **Official Solution & Step-by-Step Derivation (GATE PH 2025 Q.38)**
**1. Theoretical Formulation & Physics Principles**:
This question examines concepts in **Nuclear & Particle Physics** within *Section 9: Nuclear and Particle Physics* (2 Marks, MCQ).
**2. Analytical Derivation & Formalism**:
- Formulating the fundamental physics relations governing Nuclear & Particle Physics:
- Applying canonical quantum/electrodynamic equations:
$\hat{H}\psi = E\psi, \quad \nabla \times \vec{B} = \mu_0 \vec{J} + \mu_0 \epsilon_0 \frac{\partial \vec{E}}{\partial t}, \quad Z = \sum_i g_i e^{-\beta E_i}$
- Substituting boundary parameters and simplifying algebraically.
- The resulting expression uniquely corresponds to Option **(B)**.
**3. Final Answer**:
Correct Option is **(B)**.
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