Results 1 to 2 of 2

Math Help - Simple Harmonic Motion with Transformations

  1. #1
    Junior Member
    Joined
    Nov 2007
    Posts
    52

    Simple Harmonic Motion with Transformations

    Prove the following motions are simple harmonic and find the centre of motion, the period and the amplitude.

    1. x=2+cos 3t - \sqrt 3 sin 3t

    With this I tried to put the 2 over to the other side so that it becomes x-2=cos 3t - \sqrt 3 sin 3tand transform to R sin (3t+\alpha) but I got stuck at the transformation bit.

    2. x=6 cos^2 8t -4

    First I differentiated and got 12cos 8t (-sin 8t) which is the same as -12cos 8t sin 8t right? And I know I have to differentiate again but do I use product rule or differentiate altogether?
    Last edited by mr fantastic; June 7th 2009 at 04:44 AM. Reason: Corrected question 1.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    5
    Quote Originally Posted by nerdzor View Post
    Prove the following motions are simple harmonic and find the centre of motion, the period and the amplitude.

    [snip]

    2. x=6 cos^2 8t -4

    First I differentiated and got 12cos 8t (-sin 8t) which is the same as -12cos 8t sin 8t right? And I know I have to differentiate again but do I use product rule or differentiate altogether?
    There are a number of approaches.

    Substitute (from the double angle formula) \cos^2 (8t) = \frac{\cos (16t) + 1}{2}.

    Quote Originally Posted by nerdzor View Post
    Prove the following motions are simple harmonic and find the centre of motion, the period and the amplitude.

    1. x=2+cos 3t - \sqrt 3 sin 3t

    With this I tried to put the 2 over to the other side so that it becomes x-2=cos 3t - \sqrt 3 sin 3tand transform to R sin (3t+\alpha) but I got stuck at the transformation bit.

    [snip]
    \cos (3t) - \sqrt{3} \sin (3t) = R \sin (3t + \alpha):

    Expand the right hand side and compare witht he left hand side:

    R \sin \alpha = 1 .... (1)

    R \cos \alpha = - \sqrt{3} .... (2)

    Solve equations (1) and (2) for R and \alpha.
    Last edited by mr fantastic; June 7th 2009 at 04:47 AM. Reason: Merged posts and edited in light of correction to OP
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. [SOLVED] Simple Harmonic Motion
    Posted in the Math Topics Forum
    Replies: 4
    Last Post: September 19th 2010, 08:04 AM
  2. Simple Harmonic Motion 2
    Posted in the Calculus Forum
    Replies: 2
    Last Post: May 8th 2010, 08:55 AM
  3. Simple Harmonic Motion
    Posted in the Calculus Forum
    Replies: 2
    Last Post: May 2nd 2010, 05:22 AM
  4. Simple Harmonic Motion
    Posted in the Advanced Applied Math Forum
    Replies: 7
    Last Post: June 2nd 2008, 05:27 AM
  5. Simple Harmonic Motion
    Posted in the Trigonometry Forum
    Replies: 8
    Last Post: October 11th 2007, 11:22 AM

Search Tags


/mathhelpforum @mathhelpforum