1. Limited time only! Sign up for a free 30min personal 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!

Homework Help: Formula for the harmonic oscillator is f"(x)+W^2 * X(t)=0

  1. Nov 19, 2003 #1
    can anyboy show to me why the formula for the harmonic oscillator is f"(x)+W^2 * X(t)=0. Please I spent a whole afternoon trying to figure it out and I just wasted my time.
    Thanks
     
  2. jcsd
  3. Nov 19, 2003 #2
    Do you mean x''(t), not f''(x)?

    I'm not sure where you're starting from. Are you starting from a harmonic oscillator as something whose motion is defined by,

    [tex]x(t) = A \sin(\omega t+\phi)[/tex]

    ? If so, if you just calculate its second time derivative [tex]\ddot{x}(t)[/tex], you can see immediately that it satisfies the equation,

    [tex]\ddot{x}(t) + \omega^2 x(t) = 0[/tex]
     
  4. Nov 20, 2003 #3
    Hopefully i can get this right.

    Using the example of a mass and spring oscillator. By Newton's £rd Law the forces on the spring are equal. The forces on the spring are the force on the mass (F1=ma) and the resistive force on the spring
    (F2+-kx, negative because it is resitive and opposite to F1=ma)

    Therefore

    F1=F2
    ma=-kx
    ma+kx=0

    By definition a= x"(t)

    So mx"(t)+ kx=0
    Dividing by m gives x"(t)+(k/m)x=0

    The standard equation for the period of oscillation (T) of a mass spring
    pendulum is

    T = (2(Pi))sqrt(m/K)

    omega= w = (2(Pi))/T = 2(pi)/((2(Pi))sqrt(m/K))

    The 2(pi) should cancel and leave you with w = sqrt(K/m)
    Squaring both sides gives w^2=(K/m)

    Substitute this into the above equation and get

    x"(t) + (w^2)x = 0

    I hope thats understandable as I never tried writing such an equation in pure text before. Hope it works and helps.
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook