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!

The addition of three simple harmonic motion

  1. Sep 14, 2007 #1
    [SOLVED] the addition of three simple harmonic motion

    1. The problem statement, all variables and given/known data

    A particle is simultaneously subjected to three simple harmonic motions, all of the same frequency and in the x direction. If the amplitudes are 0.25, 0.20 and 0.15 mm, respectively, and the phase difference between the first and second is 45 degrees, and between the second and third is 30 degrees, find the amplitude of the resultant displacement and its phase relative to the first (0.25 mm amplitude) component.

    2. Relevant equations

    (the sum from i=1 to n) tan x = (the sum from i=1 to n) sin x / (the sum from i=1 to n) cos x

    Ae^(jrt) = A[cos(rt) + j sin(rt)], where j^2 = -1

    3. The attempt at a solution

    I was able to do the first part and confirm the answer in the back of the book:
    amplitude of resultant displacement ~= 0.52 mm.

    for part 2, let:
    first angle = x_1
    second angle = x_2
    third angle = x_3

    i know:
    |x_1 - x_2| = 45 degrees
    |x_2 - x_3| = 30 degrees

    thus:
    x_1 = 75 degrees + x_3
    x_2 = 30 degrees + x_3

    I was unsure how to find the resulting phase without more information about the angles. I tried to use the above tan x formula but could not get rid of the x_3 terms...
     
  2. jcsd
  3. Sep 14, 2007 #2

    learningphysics

    User Avatar
    Homework Helper

    Have you studied phasors?
     
  4. Sep 21, 2007 #3
    learningphysics,
    thanks for your help but i've solved this. i've just been too busy to post here. thanks though.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: The addition of three simple harmonic motion
Loading...