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Math Help - Simple harmonic quesion

  1. #1
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    Simple harmonic quesion

    Hi, I'm not very good at my mechanics, notably simple harmonic motion. I have been given this question:

    A particle P moves with simple harmonic motion and comes to rest at two points A and B which are 0.24m apart on a horizontal line. The time for P to travel from A to B is 1.5s.

    The midpoint of AB is O. At time t = 0, P is moving through O, towards A, with speed u m/s

    a) Find the value of u
    b) Find the distance of P from B when t = 2s
    c) Find the speed of P with t = 2s

    OKAY
    So
    a) I know T = 2pi/w, as it takes 1.5s to go from A to B, that means T=3

    Therefore w = 2pi/3
    I know v = w(a-x)
    but I don't know how that helps?

    Am I doing it right so far?

    EDIT: We are told that at t = 0 x is effectively 0, so:

    and v = u

    so u =(2pi/3)a

    But what's next? How do I find a?
    Thanks
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  2. #2
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    Quote Originally Posted by thomas49th View Post
    Hi, I'm not very good at my mechanics, notably simple harmonic motion. I have been given this question:

    A particle P moves with simple harmonic motion and comes to rest at two points A and B which are 0.24m apart on a horizontal line. The time for P to travel from A to B is 1.5s.

    The midpoint of AB is O. At time t = 0, P is moving through O, towards A, with speed u m/s

    a) Find the value of u
    b) Find the distance of P from B when t = 2s
    c) Find the speed of P with t = 2s

    OKAY
    So
    a) I know T = 2pi/w, as it takes 1.5s to go from A to B, that means T=3

    Therefore w = 2pi/3
    I know v = w(a-x)
    but I don't know how that helps?
    (a) "a" is the maximum displacement from equilibrium

    v = (2pi/3) (.12 - 0)
    v = .25 m/s

    note that the maximum speed occurs at the equilibrium position.
    max speed can also be found using this equation ... v{max} = aw

    (b) let A be at position -.12 m and B at position +.12 m

    position function ... x(t) = -.12 sin[(2pi/3)t]

    (c) velocity function ... v(t) = -.12(2pi/3) cos[(2pi/3)t]
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