Classical Mechanics (CSIR Physical Sciences): Questions 39 - 41 of 59

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Question number: 39

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

Appeared in Year: 2012

MCQ▾

Question

The Hamiltonian of a simple pendulum consisting of a mass Equation attached to a massless string of length Equation is Equation . If L denotes the Lagrangian, the value of Equation is – (December)

Choices

Choice (4) Response

a.

Equation

b.

Equation

c.

Equation

d.

Equation

Question number: 40

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

Appeared in Year: 2013

MCQ▾

Question

A pendulum consists of a ring of mass M and radius R suspended by a massless rigid rod of length Equation attached to its rim. When the pendulum oscillates in the plane of the ring, the time period of oscillation is (Dec. 2013)

Choices

Choice (4) Response

a.

Equation

b.

Equation

c.

Equation

d.

Equation

Question number: 41

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

Appeared in Year: 2013

MCQ▾

Question

Consider a particle of mass m attached to two identical springs each of length Equation and spring constant Equation (see the figure below). The equilibrium configuration is the one where the springs are unstretched. There are no other external forces on the system. If the particle is given a small displacement along the x – axis, which of the following describes the equation of motion for small oscillations?

 A particle attached to two identical springs

a Particle Attached to Two Identical Springs

In figure a particle of mass m attached to two identical springs is shown each of length l and spring constant k.

(Dec- 2013)

Choices

Choice (4) Response

a.

Equation

b.

Equation

c.

Equation

d.

Equation

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