User:Ycason

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Yale Cason is amazing.

[edit] Yale's Formulas

X = 10in

M = .0035 kg \times \frac{2.205 lbm}{kg} = 7.716 \times 10^{-3} lbm

M_{B} = .08378kg \times \frac{2.205 lbm}{kg} = 0.1847 lbm

E = 10^7\frac{lbf}{in^2}


I = \frac{bh^{3}}{12} = \frac{1.5in \times (.126in)^{3}}{12} = 2.5008 \times 10^{-4}in^4

\omega = \sqrt{\frac{3EI}{(M + .23M_{B})\times X^3}} = \sqrt{\frac{3 \times (10^7\frac{lbf}{in^2} \times \frac{32.3 lbm \frac{ft}{s^{2}}}{1 lbf} \times \frac{12in}{1ft}) \times (2.5008 \times 10^{-4})in^4}{((7.716 \times 10^{-3} lbm) + .23\times (0.1847lbm)) \times (10in)^3}} = \sqrt{57931.8s^{-2}}

\omega = \sqrt{57931.8s^{-2}} = 240.69\frac{rad}{s} \times \frac{1Hz}{2\pi \frac{rad}{s}} = 38.307Hz

Δx = Initial Displacement

f = Vibration Frequency

f(t) = \Delta x \times \cos {(2\pi (f)(t))}

f'(t) = \Delta x \times (2\pi (f)) \times -\sin {(2\pi (f)(t))}

f''(t) = \Delta x \times (2\pi (f))^2 \times -\cos {(2\pi (f)(t))}

- \Delta x \times (2\pi (f))^2 = \mbox{Max Amplitude of }f''(t) = \mbox{Max Acceleration}

- \Delta x \times (2\pi (f))^2 = -0.015m \times (2\pi (29.14\mbox{Hz}))^2 = -512.2\frac{m}{s^2}

- \Delta x \times (2\pi (f))^2 = -0.015m \times (2\pi (29.14\mbox{Hz}))^2 = -512.2\frac{m}{s^2} .164791 V .09 \mbox{Accelerometer Sensitivity}=\frac{\mbox{Volts}}{\frac{m}{s^2}} = \frac{0.074791V}{512.2\frac{m}{s^2}} = 1.46017\times 10^{-4}\frac{V}{\frac{m}{s^2}}