The parabolic coordinates (\xi ,\eta ) are related to the Cartesian coordinates (x,y) by x=\xi \eta and y=\frac{1}{2}\left( {\xi }^{2}- {\eta }^{2} \right). The Lagrangian of a two-dimensional simple harmonic oscillator of mass m and angular frequency \omega is

Oscillations — CSIR Net PYQ (Question 4)

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

Question 4 of 23 · 3.5 marks

The parabolic coordinates

(ξ, η)

are related to the Cartesian coordinates

(x, y)

x = ξ η

and

y = \frac{1}{2} (ξ^{2} - η^{2})

. The Lagrangian of a two-dimensional simple harmonic oscillator of mass

m

and angular frequency

ω

1 $\frac{1}{2} m [\hat{ξ}^{2} + \overset{η}{^}^{2} - ω^{2} (ξ^{2} + η^{2})]$
2 $\frac{1}{2} m (ξ^{2} + η^{2}) [(\hat{ξ}^{2} + \overset{η}{^}^{2}) - \frac{1}{4} ω^{2} (ξ^{2} + η^{2})]$
3 $\frac{1}{2} m (ξ^{2} + η^{2}) (\hat{ξ}^{2} + \overset{η}{^}^{2} - \frac{1}{2} ω^{2} ξ η)$
4 $\frac{1}{2} m (ξ^{2} + η^{2}) (\hat{ξ}^{2} + \overset{η}{^}^{2} - \frac{1}{4} ω^{2})$

Correct answer: Option 2

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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.