The Lagrangian of a system is given by L=\frac{1}{2}m{\hat{q}}_{1}^{2}+2m{\hat{q}}_{2}^{2}- k\left( \frac{5}{4}{q}_{1}^{2}+2{q}_{2}^{2}- 2{q}_{1}{q}_{2} \right) where m and k are positive constants. The frequencies of its normal modes are

Oscillations — CSIR Net PYQ (Question 1)

A Oscillations previous-year question (PYQ) from Classical Mechanics (CSIR Net). Read the question, check the correct answer, then practise the full topic.

Question 1 of 23 · 3.5 marks

The Lagrangian of a system is given by

L = \frac{1}{2} m \overset{q}{^}_{1}^{2} + 2 m \overset{q}{^}_{2}^{2} - k (\frac{5}{4} q_{1}^{2} + 2 q_{2}^{2} - 2 q_{1} q_{2})

where

m

and

k

are positive constants. The frequencies of its normal modes are

1 $\frac{k}{2 m}, \frac{3 k}{m}$
2 $\frac{k}{2 m} (13 \pm 73)$
3 $\frac{5 k}{2 m}, \frac{k}{m}$
4 $\frac{k}{2 m}, \frac{6 k}{m}$

Correct answer: Option 1

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This Oscillations PYQ is part of the Classical Mechanics section of CSIR Net. Browse more Oscillations questions or join the PhysicsByAaryan live batch for full conceptual coverage.