Particle in a potential well Gre. 93

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Homework Help Overview

The problem involves a particle of mass m moving in a potential well defined by two different potential energy functions: a harmonic oscillator potential for x < 0 and a linear potential for x > 0. The discussion centers around determining the period of motion for the particle at a given energy E.

Discussion Character

  • Exploratory, Conceptual clarification, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the concepts of harmonic oscillators and ballistic motion, with one participant questioning the definition of ballistic motion and seeking clarification on how to arrive at the answer.

Discussion Status

The discussion is ongoing, with participants exploring definitions and concepts related to the problem. Some guidance has been offered regarding the nature of ballistic motion, but there is no explicit consensus on the approach to solving the problem.

Contextual Notes

There is a mention of potential reliance on external resources for formulas, indicating that participants may be navigating constraints related to homework rules or the need for foundational knowledge in mechanics.

yxgao
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What concepts are involved here?
93. A particle of mass m moves in the potential shown here. The period of the motion when the particle has energy E is
The potential is V = 1/2kx^2 for x <0 and V= mgx for x > 0.

A. Sqrt[k/m]
B. 2*pi*Sqrt[m/k]
c
. 2*Sqrt[2E/(mg^2)]
D. pi*Sqrt[m/k] + 2*Sqrt[2*E/(m*g^2)]
E. 2*pi*Sqrt[m/k] + 4*Sqrt[2*E/(mg^2)]



The answer is D.
 
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Originally posted by yxgao
What concepts are involved here?

Harmonic oscillator and ballistic motion.
 
What is ballistic motion?
How do you arrive at the answer?
 
Ballistic motion is when a body moves in a field of constant gravity.

You can look up the formulae in any basic mechanics book (or basic mechanics website). Sorry, I'm really too lazy to type it all down here for you.
 

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