I\'m having trouble with a problem. I need to find the frequency of a rectangula

Question

I'm having trouble with a problem. I need to find the frequency of a rectangular cantilever beam with dimensions L=1.04m, W=0.044m, & H=0.0024m. the formula to find the frequency is w1=22.034 times the square root of (EI/pA(L^4)), where E is the Young's Modulus, I is the moment of Inertia, A=Area, L=Length, and p=density. L^4=1.04^4=1.361 and A=0.0001141m. Assume the beam is aluminum. The density of aluminum=2.7 g/mL. The E (Young's Modulus) for an aluminum cantilever beam is 10.0x10^6 psi or 69.0x10^9 N/m^2 GPa. E=stress/strain=(F/A)/(deltaL/L)

Explanation / Answer

I = w*h^3 / 12   = 0.044*0.0024^3 / (12)

frequency = 22.034 * sqrt(69*10^9 * 0.044*0.0024^3 / (12*2700 * 0.044 * 0.0024 * 1.04^4) )

                = 71.35 Hz

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