Plot the position of the particle x=Acosbt

  • #1

Homework Statement


The position of a particle as a function of time is given by x=Acosbt, where A and b are constants. The first question asks to roughly plot the position of the particle over the time interval (0,7) seconds.
The second asks what time the particle passes the origin, and what it's velocity and acceleration are at that time.
The third asks what time the particle reaches maximum distance from the origin, and what it's acceleration and velocity are at that instant.
Variables given: A=2.0m, b=1.0 radians/second

Homework Equations


N/A

The Attempt at a Solution


I got stuck in the very beginning and couldn't continue. I tried to plug in the values for the constants A and b, but upon doing so I find that I end up with cos(7 radians). I don't know how to calculate the value of cosine when I have no reference of how long one radian is.
 

Answers and Replies

  • #2
kuruman
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If b = 1 rad/s, then you have to plot 2.0(m) cos(t) where t is in seconds. Put in different values of t from 0 to 7 s and see what you get. The answer will be in meters.

On edit: Be sure to set your calculator to "radians". Radian is not a unit of time. It is dimensionless.
 
  • #3
Ray Vickson
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If b = 1 rad/s, then you have to plot 2.0(m) cos(t) where t is in seconds. Put in different values of t from 0 to 7 s and see what you get. The answer will be in meters.
Dimensionally, a cosine of a number of seconds does not exist. If you say, instead, that the time is ##t## seconds (so ##t## is |dimensionless), then ##cos(t)## is perfectly well-defined. (What may be a bit hard for the OP to grasp is that angles in "radians" are dimensionless---essentially because they are ratios of two lengths.)
 
  • #4
kuruman
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Dimensionally, a cosine of a number of seconds does not exist. If you say, instead, that the time is ##t## seconds (so ##t## is |dimensionless), then ##cos(t)## is perfectly well-defined. (What may be a bit hard for the OP to grasp is that angles in "radians" are dimensionless---essentially because they are ratios of two lengths.)
Yes, it would be less confusing if I wrote ##\cos[1(rad/s)\times t(s)]## instead.
 

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