Simple Harmonic Motion - Acceleration

[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.

 

[Doc Al]

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?

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

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

That works.

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

What's the maximum force?

 

[Peter G.]

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

 

[Doc Al]

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

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.)

 

[Peter G.]

Ok, will do!

Thanks!