# Classical Mechanics [GATE (Graduate Aptitude Test in Engineering) Physics]: Questions 44 - 47 of 84

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## Question 44

Appeared in Year: *2009*

### Question

MCQ▾The Lagrangian of a particle of mass moving in one dimension is , where and are positive constants. The equation of motion of the particle is –

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## Question 45

Appeared in Year: *2009*

### Question

MCQ▾The Lagrangian of a diatomic molecule is given by , where is the mass of each of the atoms and and are the displacements of atoms measured from the equilibrium position and . The normal frequencies are –

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## Question 46

Appeared in Year: *2009*

### Question

MCQ▾A classical particle is moving in an external potential field which is invariant under the following infinitesimal transformation –

Where is the matrix corresponding to rotation about the axis. The conserved quantities are (the symbols have their usual meaning)

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## Question 47

Appeared in Year: *2009*

### Question

MCQ▾Two monochromatic waves having frequencies and and corresponding wavelength and of same polarization, travelling along axis are superimposed on each other. The phase velocity and group velocity of the resultant wave are respectively given by –

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