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.