1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Simple harmonic motion - please help

  1. Nov 26, 2008 #1
    [tex]\pi[/tex]Hi everyone,

    I hope you can help me out with the following question. I am mainly confused about the sign

    1. The problem statement, all variables and given/known data
    A block in SHM with T= 4.0 s and A=0.1 m. How long does it take the object to move from x=0 m to x= 0.06 m.


    2. Relevant equations
    x=Acos(wt + [tex]\phi[/tex])
    w=2pi/T

    where T is period, w is angular frequency, phi is phase angle and A is amplitude.

    3. The attempt at a solution

    Using eq2, i solved for w, wich is [tex]\pi[/tex]/2.
    Then I set eq1 equal to 0. The value of phi is thus + or - [tex]\pi[/tex]/2. Since the object is assumed to be moving to the right (as it would have to if it wants to go from 0 to 0.06 m),. then we take the negative phase angle. Then, back to eq1, I put

    0.06=0.1cos(([tex]\pi[/tex]/2)t - [tex]\pi[/tex]/2)

    NOW, this is were my problem is.
    Apparently, there are then two possible answers,

    either 0.927 = ([tex]\pi[/tex]/2)t - [tex]\pi[/tex]/2, which gives 1.59 s
    or - 0.927 = ([tex]\pi[/tex]/2)t - [tex]\pi[/tex]/2. which gives 0.41 s

    Firstly, I dont understand when are we supposed to have a + and - option. Secondly, I dont trust the answer given, which is 0.41 s. Please help. :confused:
     
  2. jcsd
  3. Nov 27, 2008 #2

    Doc Al

    User Avatar

    Staff: Mentor

    Note that you can also use:
    x=Asin(wt + [tex]\phi[/tex])
    Which would eliminate the annoying phase factor, since x = 0 at t = 0:
    x=Asin(wt)

    Realize that you want the first solution after t = 0. Since t = 0 corresponds to θ = -π/2 = -1.57 radians, θ = -0.927 radians is the first solution. The +0.927 solution corresponds to the block being at x = 0.06 but going to the left. (Since the block goes back and forth, there are an infinite number of times that it's at x = 0.06; you want the first time it reaches that point.)
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Simple harmonic motion - please help
Loading...