x=3cos(50pi(t))
What is the first time after t=0 that the object reaches equilibrium?

Question

x=3cos(50pi(t))
What is the first time after t=0 that the object reaches equilibrium?

kainui · Answer

What does equilibrium mean? That's when all forces cancel each other out, so the force of the spring or pendulum here has stopped moving since if something is in equilibrium, there is no movement right? So is there a way you can find out when this is? There are at least three different ways I can think of to get the right answer, one of which doesn't even involve taking a derivative.

anonymous · Answer

Well the period of oscillation is .04 and the frequency of it is 25
Idk, if that helps.

anonymous · Answer

I don't think the amplitude helps. But that's all the information I got.

kainui · Answer

Well if you know the period of oscillation and the frequency (pretty much the same thing) then you will be able to know a what time the spring reaches its amplitude. It doesn't matter what the amplitude is, but when it's at the amplitude is when it stops moving in one direction and turns around to go the other way right? So it must have a velocity of 0 at the amplitude, meaning all the forces are in equilibrium! So at what time does it reach its first amplitude? Drawing out a little cosine wave over the course of 1 period shows us immediately when that happens.

anonymous · Answer

Is it .04?

anonymous · Answer

Because if the period is .04 that means it'll reach equilibrium again at .04

kainui · Answer

|dw:1385362164724:dw| So although you're right, it will be at equilibrium again at .04, this isn't the first time after you start that this will happen, since it has to turn around once before you complete the period, see?

anonymous · Answer

so .02?

kainui · Answer

Yeah, I believe so. =D

kainui · Answer

Ok I just calculated the period for myself, now I know so. .02 seconds.

anonymous · Answer

It was incorrect.

anonymous · Answer

:(

anonymous · Answer

Ughhh

kainui · Answer

Wait a second. I interpreted this question as meaning the equilibrium of _forces_ not the spring's point of equilibrium... Slightly different, sorry.

kainui · Answer

This is even easier. The equilibrium of the spring is when it's not stretched or compressed at all. So this is when the displacement is 0, right? |dw:1385363501003:dw|