Consider a mass mounted on the end of a cantilever beam. Assume that the end-mass is much greater than the mass of the beam.

where,

E: the modulus of elasticity = 29000 kip/in²

I: the area moment of inertia = 1728 in⁴

L: the length = 10000 in

g: gravity = 386.0886 in/sec²

m: mass = 0.0005 kip-sec²/in

Equation of motion for free vibration of a SDOF system:

md²u/dt²+ ku=0

d²u + W_n²u=0

Then, the natural frequency of vibration, W_n= √k/m

The stiffness at the end of the beam, k= 3EI/L³ → k= 1.50336e-4 kip/in²→ W_n= 0.548 rad/sec

The natural period of vibration, T_n= 2π/W_n → T_n= 11.459 sec

App

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Result Comparison

	Independent	OpenBrIM	Percent Difference (OpenBrIM vs Independent)
T₁ (sec)	11.4586	11.4574	0.010%

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