GR | # Login | Register
  GR8677 #60
GREPhysics.NET Official Solution    Alternate Solutions
Verbatim question for GR8677 #60
Mechanics}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).

See below for user comments and alternate solutions! See below for user comments and alternate solutions!
Alternate Solutions
There are no Alternate Solutions for this problem. Be the first to post one!
2016-09-20 02:36:59
Easy, but even easier if you look at it this way: a is absolutely meaningless because the zero of potential is arbitrary. So it\'s exactly like the mass-on-a-spring model.NEC
2010-11-11 23:02:29
Force is the negative gradient of potential energy. The a drops out.
2013-09-26 08:41:23
but this is asking for the frequency, how does force and frequency relate?
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).
2010-09-21 06:25:37
i totally agree, to be sure that it doesn't depend on a, just remember that shifting the potential energy by a constant cannot change the motion (classically) so it doesn't affect the frequency.

Post A Comment!
Click here to register.
This comment is best classified as a: (mouseover)
Mouseover the respective type above for an explanation of each type.

Bare Basic LaTeX Rosetta Stone

LaTeX syntax supported through dollar sign wrappers $, ex., $\alpha^2_0$ produces .
type this... to get...
$\langle my \rangle$
$\left( abacadabra \right)_{me}$
The Sidebar Chatbox...
Scroll to see it, or resize your browser to ignore it...