Phase diagrams

Classical Mechanics Level 3

Let a particle with non-zero velocity at the lowest point of its trajectory, in one dimension, be under the influence of a potential

$V(x) = kx^4,$

where $k$ is some real positive constant and $x$ the position of the particle. If $A$ is the least upper bound for the values of the position of this particle, then the period of the movement is proportional to

1/A

A^3

it does not depend on

A

1/A^3

A

1 solution

Karan Chatrath
Feb 3, 2019

The following steps show how the integral is approached:

Your substitution cannot be made since

$\cos(\theta) d \theta = \frac{2x}{A^2} dx.$

A Former Brilliant Member - 2 years, 4 months ago

Hey Lucas, I have made an edit to my solution. It shows the steps involved while computing the integral. Hope this helps.

Karan Chatrath - 2 years, 4 months ago

Sorry, I didn't see the last paragraph of your solution. It is correct, then. :)

A Former Brilliant Member - 2 years, 4 months ago

Phase diagrams

1 solution

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