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Homework Help: Error in Natural Frequency (Lab)

  1. Oct 31, 2015 #1
    So I just did a lab on resonant frequency, and have to find the error of the period: $$T = 2π\sqrt{m/k}$$
    m and k were measured with an error of Δm and Δk. My teacher didn't explain well how to do errors, so I just want to know if I did this right.

    Prorogation of Error equations:
    $$y=x^n ⇒ Δy=nx^{n-1}Δx$$ $$y=x_1/x_2 ⇒ Δy=y\sqrt{(Δx_1/x_1)^2+(Δx_2/x_2)^2}$$

    Attempt at solution:
    $$Δ(m/k)^{0.5}=0.5(m/k)^{-0.5}Δ(m/k)$$ $$Δ(m/k)=(m/k)\sqrt{(Δm/m)^2+(Δk/k)^2}$$ $$ Therefore, ΔT = 2π * 0.5(m/k)^{-0.5}(m/k)\sqrt{(Δm/m)^2+(Δk/k)^2}=π\sqrt{(Δm)^2/(mk)+(m(Δk)^2)/k^3}$$
     
    Last edited: Oct 31, 2015
  2. jcsd
  3. Oct 31, 2015 #2

    mfb

    User Avatar
    2017 Award

    Staff: Mentor

    Right.
    The expression gets easier if you write down ##\frac{\Delta T}{T}##.
     
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