Can someone help me linearise this equation?
I need to linearise this equation in physics. I have the data points for f and for h. I know what f0 is too. I don't know what a and n are though. Someone pls help! Ps. f is there frequency of a resonance and h is the height of the water in the glass.
- JOHNLv 78 months ago
f = √[f₀²/(1 + αhⁿ)]
f² = f₀²/(1 + αhⁿ)
f₀²/f² = 1 + αhⁿ
f₀²/f² - 1 = αhⁿ
log(f₀²/f² - 1) = logα + log(hⁿ)
log(f₀²/f² - 1) = logα + nlogh
Plot log(f₀²/f² - 1) against logh
You should get a straight line,
lope n and y-intercept logα,
from which you can read off
n and logα.
- MorningfoxLv 78 months ago
You can linearize it as f = linear function of (f0), or
f = linear function of (alpha), or (h), or (n). You didn't say which one of these is your goal. I will assume that it is "h".
One of the first steps is to decide what value of (h) you want to center your function around. Then the linear form is f = A + B*( h - center), with A = value of f when h = center.
The next step is to figure out how much f changes, for a small change in "h". That will give you the value of "B".