1) Given the two beams (Aluminum and steel) (0.125"X 1"X 20"), with the following material properties: For Steel E = 206.8 (10^9) Pa and ρ = 0.7830 kg/cm. E= 30X10^6 psi, ρ =0.00074 lb/ft 

For Aluminum: E = 73 (10^9) Pa and ρ = 0.2750 kg/cm

E=10.6(10^6) psi and ρ = 0.00026 lb/ft

The resonant frequencies for a simple cantilever beam is given by

w= natural frequency in cycles per second

E = modulus of elasticity of the material in psi

I = moment of inertia in inches4

L =length in inches

ρ = mass per unit length , for steel =0.284/(12*32) =0.00074 lb/ft or 0.7830 kg/cm

For aluminum ρ = 0.1/(12*32) =0.00026 lb/ft or .275kg/cm Cn = coefficient for the different resonant modes ( C1 = 3.52, C 2 = 22.4, C 3 = 61.7 )

Calculate the first three natural frequencies using the above equation.

2) Are the number of degrees of freedom of a system and the number of its norm al modes related? If so, how?

3) How can a normal mode be recognized physically?

4) What data will you record during the lab?

5) What observations will you make?

6) What do you expect to happen when you drive a system at one of its natural frequencies?

Attachment:- 319562_3_ibrahem--1- (1).xlsx