GREPhysics.NET: GR8677 #60

GR8677 #60

Problem

GREPhysics.NET Official Solution

Mechanics $\Rightarrow$ }Simple Harmonic Motion

Recall $F=-\frac{\partial V}{\partial x}=-2bx$ . Simple harmonic motion has the simple form, $\ddot{x}\propto x$ . Thus $F=m\ddot{x}=-2bx \Rightarrow \ddot{x}=-\omega^2 x$ , where $\omega^2=2b/m$ is the frequency squared. Thus, simple harmonic motion occurs with a frequency determined by both $b$ and $m$ . This is choice (C).

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Comments

sirius
2008-11-05 22:26:45

A similar solution if you remember $V(x) = \frac{1}{2}m\omega^2x^2$ . The given V(x) has a vertical shift, a, which can be ignored by shifting your zero-point energy. So, $b=\frac{1}{2}m\omega^2$ , solving for $\omega$ makes it depend on b and m.

This is enough, but the problem asks for frequency $f=\frac{\omega}{2\pi}$ . So $f=\frac{1}{2\pi}\sqrt{\frac{b}{2m}}$ . making f depend on b and m. The answer then is (C).

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