# Simple Harmonic Motion - Acceleration

1. Jun 28, 2011

### Peter G.

Hi,

Assuming that the motion of the hydrogen atom is simple harmonic, its frequency of oscillation, f, is given by the expression:

f = 1 / 2π * √(k/m)​

where k is the force per unit displacement between a hydrogen atom and the carbon atom and the m is the mass of a proton.

(i) Show that the value of k is approximately 560 N/m
(From previous parts of this question I knew: f = 9.1 x 1013 Hz and the mass was 1.7 x 10-27

I managed to do this question by rearranging and plugging the numbers in the formula

However, I am having problems with part (ii)

(ii) Estimate, using your answers to (c)(i), the maximum acceleration of the hydrogen atom.

I am thinking either F = ma, where F = kx. In this case, the k I got from the previous question would be the constant k, or the F itself?

Or use a = -ω2x, using the maximum displacement (I have it from previous part of the question)

How should I approach the second part with the F = ma format? Is it possible to tackle the problem in those two ways?

Thanks,
Peter G.

2. Jun 28, 2011

### Staff: Mentor

That method would work, but I don't understand the question. (Of course the k will be the constant k.)

That works.

What's the maximum force?

3. Jun 28, 2011

### Peter G.

The maximum force would be the constant multiplied by the maximum displacement?

4. Jun 28, 2011

### Staff: Mentor

Exactly. Now you can use Newton's 2nd law to calculate the maximum acceleration.

(Be sure to solve it both ways--convince yourself that the methods are equivalent.)

5. Jun 28, 2011

Ok, will do!

Thanks!