Central Force (period of revolution and period of small radial oscillations)

In summary, the conversation discusses finding the period of revolution and small radial oscillations for a particle with mass m and angular momentum L moving in a central force V=(1/2)kr^2 (k>0). The homework equations and attempted solution using Lagrange were mentioned, but the person got lost. They are seeking help to distinguish the expressions for the two periods. The response suggests looking for the radius at the potential minimum to find the key to solving for the periods.
  • #1
noramire
4
0
1.
A particle of mass m and angular moment L moves in a central force V=(1/2)kr^2 (k>0).
Find the period of revolution for the circular movement and the period of small radial oscillations around the stable cicular orbit.

Homework Equations




The Attempt at a Solution


Well I tried using Langrange and then applied the conditions of a circular but I get lost. Any help would really help, especially if someone could help me distinguish the expressions for the two periods. Thanks.
 
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  • #2
Hi noramire and welcome to PF. Please follow the rules of this forum and use the template when you seek help with homework. Show us in some detail what you have done so that we can help you by pointing out where you might have gone wrong.
 
  • #3
Yeah sorry abour the noob mistake. I actually really didn't know where to get started, you know. But I think I got it now...Circular orbit implies radius at Potential Minimum, I think that is the key to finding the radius then using common expressions for period of rev and period of radial oscillation.

Thanks, and again sorry.
 

What is Central Force?

Central Force is a type of force that acts towards a fixed point or center. It is also known as a radial force. Examples of central forces include gravitational force and electrostatic force.

What is the period of revolution in the context of Central Force?

The period of revolution in the context of Central Force refers to the time it takes for an object to complete one full revolution around a fixed point or center under the influence of a central force. It is generally denoted by T and is dependent on the mass of the object, the magnitude of the central force, and the distance from the center.

How is the period of revolution calculated?

The period of revolution can be calculated using the formula T = 2π√(m/rF), where T is the period, m is the mass of the object, r is the distance from the center, and F is the magnitude of the central force.

What is the period of small radial oscillations in the context of Central Force?

The period of small radial oscillations refers to the time it takes for an object to complete one oscillation around its equilibrium point, which is at a fixed distance from the center, under the influence of a central force. It is denoted by T' and is dependent on the mass of the object, the magnitude of the central force, and the distance from the equilibrium point.

How is the period of small radial oscillations calculated?

The period of small radial oscillations can be calculated using the formula T' = 2π√(m/F'), where T' is the period, m is the mass of the object, and F' is the magnitude of the restoring force, which is equal to the central force at the equilibrium point.

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