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If i know velocity, then i know acceleration right?

  1. Jan 11, 2005 #1
    For velocity at a certain particle in a simple harmonic oscillation is the following:

    v= w (anguluar frequency) times the squareroot of A^2-x^2

    but if i wanted to find the acceleration at a certain particle in a simple harmonic oscillation, i can somehow derive a formula from the above equation right? But how would u derive it?

    I know that that V= dx/dt ..and a= (d^2)x/dt^2

    ugh, i forgot my calculus, anyone clear it up for me?

    thanks
     
  2. jcsd
  3. Jan 11, 2005 #2
    for simple hamonic motion
    [tex] x = A \sin{( wt-\theta)} [/tex]
    I have no idea what is your equation looks like

    v= w (anguluar frequency) times the squareroot of A^2-x^2 :confused:

    put it in Latex pls.....
     
  4. Jan 11, 2005 #3

    dextercioby

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    The equations for linear harmonic oscillator are something like that
    [tex] x(t)=A\sin(\omega t+\phi)[/tex]
    [tex] v_{x}(t)=A\omega\cos(\omega t+\phi) [/tex]
    [tex] a_{x}(t)=-A\omega^{2}\sin(\omega t+\phi) [/tex]

    Then decide what are the initial conditions.And u can determine the 2 unknowns;

    Daniel.
     
  5. Jan 11, 2005 #4
    [tex] v= w \sqrt{A^2-x^2} [/tex] is that what you trying to say???
     
  6. Jan 11, 2005 #5
    OKAY, i dunno where did you get this equation.... this is right but ppl usually don't write it this way, if you wanna find a(t) from your equation, substitude v=dx/dt, you have
    [tex] dt=dx/ (w \sqrt{A^2-x^2}) [/tex]
    integrate both side and you will have[tex] x(t) = Asin(wt+\theta)[/tex]
    after you have x(t), everything should be easy
     
  7. Jan 11, 2005 #6
    yes,

    [tex] v= w \sqrt{A^2-x^2} [/tex]

    is what i am trying to say, so how can u derive a formula from the above equation for acceleration? that is my question
     
  8. Jan 11, 2005 #7
    did i just tell you.. do the integral and find x(t)
    after you have x(t), v(t)= dx/dt, a(t) = dv/dt
     
  9. Jan 11, 2005 #8

    dextercioby

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    The formula is deduced from applying the law of energy conservation.Once u integrate this ODE (using the method prescribed above),you need to diff.2 times wrt to time to find the acceleration.

    Daniel.
     
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