Classical Mechanics-Lagrangian and Hamiltonian Formalism and Equations of Motion (CSIR (Council of Scientific & Industrial Research) Physical Sciences): Questions 7 - 10 of 16

Question

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

Question

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

Question

Consider a particle of mass m attached to two identical springs each of length and spring constant (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?

(Dec- 2013)

Question

A particle of mass ‘m’ moves inside a bowl. If the surface of the bowl is given by the equation where, is a constant, the Lagrangian of the particle is: (December)