Solving Military HW: Position & Speed at Time 0s

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The discussion revolves around solving a physics problem related to simple harmonic motion (SHM) involving military hardware with a specified amplitude and frequency. The key equations for position and velocity in SHM are provided, with the position equation being x = 23sin(346t). To find the time when the system passes through 15cm, users are advised to isolate sin(346t) and use the inverse sine function. The relationship between velocity and position is also mentioned, but there is confusion regarding the calculation of time and the meaning of certain variables. Overall, the participants are seeking clarification on applying trigonometric functions to SHM problems.
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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.
 
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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.
 
jimmy42 said:
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.
 
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