Physics

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I'm haivng troulbe proving the deriviation of this formula on my own...

could you please help me derive the proof of the formula or maybe show me one thansk...

I need to prove this formula

period of a mass spring system in simple harmonic motion

T = 2 pi square root of (m/k)
period = 2 pi X square root of (mass divided by spring constant)

thanks

  • Physics -

    F = m a
    F = -k x for spring of constant k in N/m
    so
    m a = - k x
    now assume motion of form x = A sin (2 pi f t)
    then
    dx/dt = velocity = A (2 pi f) cos 2 pi f t)
    then
    d velocity/dt = a = -A (2 pi f)^2 sin (2 pi f t)
    or in other words
    a = - x (2 pi f)^2
    so
    - k x = m [ - x (2 pi f)^2 ]
    or
    (2 pi f)^2 = k/m
    so
    2 pi f = sqrt (k/m)
    but T = 1/f
    so
    T = 2 pi sqrt (m/k)

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