Cantilever beam motion decay equivalent system question Theoretically Equivalent

Question

Cantilever beam motion decay equivalent system question

Theoretically Equivalent System. The system that will be examined in this lab is a simple cantilever beam with a mass attached to the beam tip. The fundamental mode of vibration of the cantilever beam can be modeled as a single degree of freedom vibrating system with lumped inertia and stiffness. The system is similar in many ways to a mass attached to a spring, shown in Figure 1. See Figure 8 for a schematic of the experimental setup used as well. equivalent Ma system Meq Meq 0.23Mb+Ma

Explanation / Answer

Given,

x=Xsin(wt)

and at a certain point X= 2 mm

T= period = 0.015 sec

so w= (2*pi)/T = (2*3.141)/ 0.015 = 418.8 rad/s

now, as x= Xsin(wt)

velocity v= dx/dt = XwCos(wt)

acceleration a = dv/dt = - Xw2sin(wt)

so acceleration amplitude = w2X = 418.82*0.002

so acceleration amplitude = 350.8 m/s2

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