Spring Calibration Data -> Need to figure out formula

mcdowellmg
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Spring Calibration Data --> Need to figure out formula

I feel like every time I post a problem here, I end up figuring it out. So, thanks for that! haha
 
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Another question. I am supposed to find the expected slope of a line that will help me realize that ac = rω2.

expected slope = –4*pi^2(µ/g)(Mg/k) =

I know that (Mg/k) = 5.3. I know that µ = 5. I am GUESSING that g = 9.8 or -9.8, but both of the answers 106.753 or -106.753 are not correct. I cannot figure this out, so thanks for any help!
 
Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...
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