Classical MechanicsLagrangian 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
Appeared in Year: 2011
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
Appeared in Year: 2016
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
Appeared in Year: 2016
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
Appeared in Year: 2016
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. 
