User:Ycason

$$R \theta dot $$

Yale's Formulas
$$X = 10in$$

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

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

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

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

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

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

$$\Delta x = \mbox{Initial Displacement}$$

$$f= \mbox{Vibration Frequency}$$

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

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

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

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

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

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