# Classical Mechanics-Lagrangian and Hamiltonian Formalism and Equations of Motion (CSIR (Council of Scientific & Industrial Research) Physical Sciences): Questions 11 - 14 of 16

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## Question number: 11

» Classical Mechanics » Lagrangian and Hamiltonian Formalism and Equations of Motion

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Appeared in Year: 2011

MCQ▾

### Question

The Hamiltonian of a particle of unit mass moving in the XY – plane is given to be:

in suitable units. The initial values are given to be and . During the motion, the curves traced out by the particles in the xy – plane and the plane are (June)

### Choices

Choice (4)Response

a.

a hyperbola and an ellipse, respectively

b.

a straight line and a hyperbola respectively

c.

both straight lines

d.

both hyperbolas

## Question number: 12

» Classical Mechanics » Lagrangian and Hamiltonian Formalism and Equations of Motion

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Appeared in Year: 2016

MCQ▾

### Question

The Hamiltonian of a system with generalized coordinate and momentum is . A solution of the Hamiltonian equation of motion is – (in the following and are constants) (June)

### Choices

Choice (4)Response

a.

b.

c.

d.

## Question number: 13

» Classical Mechanics » Lagrangian and Hamiltonian Formalism and Equations of Motion

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Appeared in Year: 2016

MCQ▾

### Question

The dynamics of a particle governed by the Lagrangian describes: (December)

### Choices

Choice (4)Response

a.

a damped harmonic oscillator with a time varying damping factor

b.

an undamped simple harmonic oscillator

c.

a free particle

d.

an undamped harmonic oscillator with a time dependent frequency

## Question number: 14

» Classical Mechanics » Lagrangian and Hamiltonian Formalism and Equations of Motion

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Appeared in Year: 2016

MCQ▾

### Question

The parabolic coordinates are related to the Cartesian coordinates by and . The Lagrangian of a two – dimensional simple harmonic oscillator of mass and angular frequency is: (December)

### Choices

Choice (4)Response

a.

b.

c.

d.

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