# Period Sinusx

#### curicuri

##### New member
Hi again. Could someone help me out with a an assignment?

Problem
Harmonic motion
A=5 cm
Figure shows the kinetic energy of the stone in motion. At 0,45 s the stone is below the state of equilibrium, determine how long from the equilibrium the stone is located at this time.

My question

They claim in the answer that the period from one top the next is a half period. What I have learned is that the distance between two peaks are a full period (360 degrees). Then I started to think about that the y-axis is measured in energy and not in length or velocity. Could this has something to do with that the period now is different?

#### Attachments

• 18.1 KB Views: 2

#### Subhotosh Khan

##### Super Moderator
Staff member
Hi again. Could someone help me out with a an assignment?

Problem
Harmonic motion
A=5 cm
Figure shows the kinetic energy of the stone in motion. At 0,45 s the stone is below the state of equilibrium, determine how long from the equilibrium the stone is located at this time.

View attachment 12518

My question
They claim in the answer that the period from one top the next is a half period. What I have learned is that the distance between two peaks are a full period (360 degrees). Then I started to think about that the y-axis is measured in energy and not in length or velocity. Could this has something to do with that the period now is different?
Correct.

However, the period is not different - it is the measurement that is different.

#### Dr.Peterson

##### Elite Member
Problem
Harmonic motion
A=5 cm
Figure shows the kinetic energy of the stone in motion. At 0,45 s the stone is below the state of equilibrium, determine how long from the equilibrium the stone is located at this time.
I think you need to state the entire problem. You haven't told us what "the stone" is and what is happening to it, what "A" means, and so on. Then you asked only about one bit of the explanation of the solution, without showing anything else.

There are a couple translation issues; I think "how long" is supposed to be "how far", and I'm not sure what "below the state of equilibrium" means. That's another reason to state the entire problem, providing more context for our interpretation.

As for the half-cycle part, we need the context. My suspicion is that you have missed the fact that the energy is related to the square of velocity (or something of that sort), and squaring a sinusoid halves the period - so the period they are talking about is not the period of the energy, but the period of velocity or position or something like that.

#### curicuri

##### New member
Aha sorry. The info that is missing is:
1) A=amplitude
2) how far
3) The stone is put on a spring. Then it is pulled so that it is set in a harmonic motion.
4) The equilibrium state is the initial position of the stone before it is pulled. When the stone is set in motion, this position would be where the velocity is max.

What your are saying about the half-cycle part sounds tricky. Now when I supplemented info, is there another way you could try to explain this to me perhaps?

#### Dr.Peterson

##### Elite Member
I would hope that somewhere they explained the halving of the period!

Are you aware that $$\displaystyle \sin^2(t) = \frac{1 - \cos(2t)}{2}$$ ? That's what I'm referring to, and that's just what the given graph looks like.

Again, it might be easier to explain things if we could see the entire text of the answer (in English, unfortunately; I know a little Swedish, but not enough). Then I could be sure how they are approaching the details, and refer to that in explaining things.

#### curicuri

##### New member
You are right. They explain this, but I fail to grasp it. Anyway, I feel I need to move on to other assignments, perhaps I get back to this one later. Thank you very much for doing your best to help me, in Swedish thanks=tack. Tack!

#### Dr.Peterson

##### Elite Member
Varsågod.

I hope you will come back to it; it's probably not central to what you are learning, but it may turn out to be important sometime soon.