Finding angular velocity based on x vs t graph

[cuttooth]

Homework Statement

I am given the attached graph (excuse my abysmal homemade graph!). On the y-axis, I presume that it is displacement (x). The x-axis is time. This graph looks like SHM, but I could be wrong! The graph rises from 0 to 2 every 2 seconds, and drops back to 0 on the y-axis for 2 seconds before repeating the cycle. The problem asks to find angular velocity based on the graph. I am given the choices of 2.0 rad/s, 0.5 rad/s, 1 rad/sec, or none of above.

Homework Equations

This graph looks like SHM, but I could be wrong!

The Attempt at a Solution

I really have no clue how to derive angular velocity based on this graph. I am guessing you have to find tangential velocity from the graph and from there determine angular velocity using the formula v(tangential) = ω r. Am I on the right track? Again, please excuse the poor graph. :)

 

[kjohnson]

That graph can't be a x(t) plot because of the verticle segments. This says that somhow a particle covered some distance x in zero time. Also the velocity is undefined at those points. If you were just looking at it on a cycle or periodic basis then you would say it completes 1 cycle in 4s. And in one cycle there are 6.28rads. So you would get 1.57rad/s which would be none of the above.

 

[kerimek]

I would first clarify the units of the y-axis to ensure that it is indeed displacement (x) and not something else. Then, I would plot the graph in a computer program or use a ruler to measure the data points and create a more accurate graph. From there, I would analyze the graph to determine if it is indeed simple harmonic motion (SHM) or not. If it is SHM, then I would use the equation x = A cos(ωt) to find the angular velocity (ω) by comparing the graph to this equation. If it is not SHM, then I would use other equations or methods to find the angular velocity. It is important to also consider the given choices and see if any of them match with the calculated angular velocity. If none of the choices match, then it is possible that the graph does not accurately represent the data or there may be an error in the calculations. Overall, it is important to thoroughly analyze the graph and use appropriate equations and methods to accurately determine the angular velocity.