# Simple harmonic motion question

1. Nov 2, 2014

### pyman999

1. The problem statement, all variables and given/known data
http://puu.sh/cAjmp/14ba3df23a.jpg [Broken]

2. Relevant equations
Acceleration at any instant: -(2*pi*f)^2 * x, where x is displacement from equilibrium and f is frequency.

3. The attempt at a solution
Firstly, I know it can't be D as acceleration would increase as potential energy increases, it also can't be B as acceleration is 0 when velocity is at a maximum, or "1", so it isn't in the opposite direction.

Where I am confused is at A and C, as they both seem correct to me. When the particle's speed is greatest is when it is passing through equilibrium, and so acceleration will be 0, its least value. But as acceleration is -(2*pi*f)^2 * x, you can say that acceleration is proportional to the frequency. Therefore, they are both right? But the answer is A only.

Last edited by a moderator: May 7, 2017
2. Nov 2, 2014

### BvU

Hello Py, welcome to PF :)

You have correctly eliminated B and D. In C, the word "proportional" means that if one doubles, the other doubles too. That there is a factor f in the expression isn't enough: netto there has to be one factor f only.

Voting goes strongly to answer A: with $a = {dv\over dt}$ and the second one is zero at points where the speed is greatest, meaning the magnitude of a is then zero.

3. Nov 2, 2014

### pyman999

Thank you, this cleared it up.