Particle in a potential well Gre. 93

AI Thread Summary
The discussion centers on the motion of a particle in a potential well defined by two regions: a harmonic oscillator for x < 0 and ballistic motion for x > 0. The period of motion for a particle with energy E is determined to be option D, which combines elements of both harmonic and ballistic motion. Key concepts include the behavior of particles in varying potential fields and the formulas associated with harmonic oscillators and ballistic trajectories. The conversation emphasizes the need for understanding basic mechanics principles to derive the answer. Overall, the thread highlights the integration of different motion types in analyzing particle dynamics in potential wells.
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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