Question : Find out the total energy of earth in its circular orbit around the sun in terms of gravitational constant Answer: Let R be the total distance between the earth and the sun. If

# CSIR

## Brachistochrone Problem

Question

If a particle falls from rest under the influence of gravity from higher to lower point in the minimum time, what is the curve that the particle will follow?

Solution

Suppose v is the speed of the particle along the curve, then in traversing ds portion of the curve time spent would be

## Equations of motion of coupled pendulum using the lagrangian method

Question

Obtain the equations of motion of coupled pendulum using the lagrangian method.

Solution

Consider a system of coupled pendulums as shown below in the figure