# Find the Position

## Homework Statement

A system is testing some military HW which has an amplitude of 23cm and frequency of 55Hz. At time 0s it is at the origin.

## Homework Equations

At what time does it pass through 15cm?
When the speed is 200ms^-1 what is the position?

## The Attempt at a Solution

omega = (2pi) * 55 = 346 r^s-1
max V = 23 * 346 = 7958 -- is that right??

To find the time, do I need to use trigonometry and the unit circle? No clues about the second one. Can SHM problems be found with the unit circle? Do I need to only use the SHM equations?

Should I think SHM in terms of the unit circle or movement going only up and down and not in a circle at all?

I'm really stuck, thanks for any help.

## The Attempt at a Solution

rock.freak667
Homework Helper
You have that x=Xsin(ωt+φ) and you found that ω=346 rad/s and φ=0, X=23.

Hence you have x = 23sin(346t).

So when x=15, you just need to use standard trigs.

siny=a ⇒ y=sin-1(a)

For the second one, velocity 'v' is related to 'x' by v = dx/dt.

Sorry, I don't get it.

What is a? I looked at that first equation but how do I find t from that?

Thanks,

Jim.

rock.freak667
Homework Helper
Sorry, I don't get it.

What is a? I looked at that first equation but how do I find t from that?

Thanks,

Jim.

x = 23sin(346t).

then you have 15=23sin(346t). Make sin(346t) the subject and then take the inverse sine of that.