Particle in a potential well Gre. 93

[yxgao]

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.

[arcnets]

Originally posted by yxgao
What concepts are involved here?

Harmonic oscillator and ballistic motion.

[yxgao]

What is ballistic motion?
How do you arrive at the answer?

[arcnets]

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.