# Homework Help: Simple Harmonic Problem 2

1. Dec 13, 2012

Hi friends the problem is -

https://fbcdn-sphotos-d-a.akamaihd.net/hphotos-ak-prn1/30370_2656498989013_1471109032_n.jpg

Attempt -

friends as per the question I am trying to get the acceleration- displacement equation for this problem. So I am using

F = - (dU / dx)
Differentiating Potential energy function w.r.t. x I get,

F = - (2a + 4b .x3)

But F = mass. acceleration so,

acceleration = - (2a/m + 4b/m x3)

Now I am sticking here that how to proceed further to get the result like,

acceleration = - ω2 . x

Please friends help me in solving this Problem.

2. Dec 13, 2012

### TSny

Check to make sure that you took the derivative of ax2 correctly. Also keep in mind that you are considering "small" oscillations.

3. Dec 14, 2012

F = - (dU / dx)
Differentiating Potential energy function w.r.t. x I get,

F = - (2ax + 4b .x3)

But F = mass. acceleration so,

acceleration = - (2a/m.x + 4b/m x3)

It is for small oscillations so x3 will be neglected.

Hence accn = -(2a/m).x

acceleration = - ω2 . x

hence The answer comes, ω = √(2a/m)

Yet the answer is not achieved. In the book the answer is option (B)

4. Dec 14, 2012

### TSny

I think you got the right answer. I don't see how (B) could be the answer.

5. Dec 14, 2012

Yes there is mistake in the answer of book.