Simple Harmonic Motion question.

[gabloammar]

Homework Statement

We say that the equation a= ω²x defines simple harmonic motion - it tells us what is required if a body is to perform s.h.m. The equation x= x_osinωt is then described as a solution to the equation, since it tells us how the displacement of the body varies with time. If you have studied calculus you may be able to differentiate the equation for x twice with respect to time to obtain an equation for acceleration and thereby show that the defining equation a = -ω²x is satisfied.




2. The attempt at a solution

I haven't done calculus as I haven't taken Math as a subject. I wanted to ask if it would be possible to understand that statement without taking calculus. Or if someone could explain to me what the whole point of the statement is. I really don't get it at all. Do tell me if I have to study a bit of calculus to understand this, because I will if I have to. Thanks :)

 

[JHamm]

Doing physics without taking calculus seems to be somewhat like welding without your hands (though this depends on what level of physics you're doing), if you plan on going very far calculus is a must though.
The paragraph is saying that an object going in simple harmonic motion has an acceleration given by $a = \omega ^2 x$ and that if you do some calculus you can see that the equation of the position of that object is given by $x = x_0 \sin \omega t$.
The actual calculus involved (differentiation) allows you to take the function of position and use that to find the velocity then use that to find the acceleration, and if you use the x function given to you then they're just telling you that it all works out nicely :)
The take home points are really just that objects in SHM move according to $x = x_0 \sin \omega t$ and have an acceleration at a position x given by $a = \omega ^2 x$.

 

[gabloammar]

Thanks a LOT for that! Seriously :)

I'm doing A-Level/12th Grade physics [which the syllabus says DOES require a little bit of math i.e. differentiation, integration and the know-how of logarithms] but I don't take mathematics as a subject because I'm aiming to get into med school, plus I absolutely hate math so I didn't pursue it further. But I understood what you said.

Just as a precautionary measure though, I'll learn differentiation and then come back to this statement again. Bet I'll understand it even better then. Thanks again!

 

[ehild]

Homework Statement

We say that the equation a= ω²x defines simple harmonic motion - it tells us what is required if a body is to perform s.h.m. The equation x= x_osinωt is then described as a solution to the equation,

It is not true: a minus sign is missing.
a=-ω²x is valid for the simple harmonic motion.


ehild

 

[gabloammar]

It is not true: a minus sign is missing.
a=-ω²x is valid for the simple harmonic motion.


ehild

Yeah yeah sorry, typo. Thanks for correcting it.