Was this Maths Question Poorly Worded?

[uart]

I was going through a previous years maths test and came up against one particular question in which I couldn't quite figure out exactly what was being asked.

The question was worded exactly as follows :
"A particle moves in a straight line with it's position at time $$t$$ being given by $$x = 4 \sin(2t + \pi/3)$$. Show that the particle is undergoing simple harmonic motion."

To me the most fundamental definition of SHM is that the displacement is a sinusoidal time function, so the question seemed kind of pointless, or at best trivial. Apparently the examiner wanted you to show that acceleration is proportion to the negative of the displacement and say "therefore it's SHM". That's fine, I agree that the this also implies SHM, but isn't the sinusoidal time function even more fundamental?

Does anyone else think this was a badly worded exam question?

 

[matt grime]

Not at all, in my experience the definition of SHM *is* that acceleration is -kx for some positive k and x the displacement. It is not sinusoidal by definition, it is merely that sin is the function that will satisfy that differential equation (or cos, or a combination of both depending on initial conditions)

and remember that an exam is written to test an syllabus that will state what *their* definition of SHM will be for that course.

 

[tacman]

It is difficult to say definitively whether this maths question was poorly worded or not without more context. However, based on the information provided, it does seem that the question could have been clearer and more specific in what it was asking for.

The question asks students to show that the particle is undergoing simple harmonic motion, but does not specify what exactly needs to be shown or proven. As the student mentioned, there are multiple ways to demonstrate that the particle is undergoing SHM, such as showing a sinusoidal displacement function or the proportional relationship between acceleration and displacement.

In this case, it seems that the examiner was looking for a specific approach to proving SHM, which may have caused confusion for students who may have used a different method. Additionally, the use of "therefore" in the given solution implies that the examiner was expecting a specific conclusion to be drawn from the shown work, which may not have been clear from the wording of the question.

Overall, while the question may not have been poorly worded, it could have been more specific and clear in its expectations to avoid confusion and ensure that students are demonstrating their understanding accurately.