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The first 200 words of this essay...
M3 Vibrating Beam
The aim of this experiment was to determine the response of a spring-mass-dashpot system to a disturbance and investigate the phenomena associated with the vibration of a beam.
Moments about pivot neglecting mass of beam
Mx1L1 + Cx3L3 + Kx3L3 =0
Including mass of the beam
(I/ (L1) ^2 + M) x1L1 + Cx3L3 +Kx3L3 =0
To find I the inertia of the beam
I = (m (L^2))/3
Where for the above
M=mass of weight
X1=amplitude of oscillation
X3= amplitude of oscillation
L1= length from the mass
L2= length from the mass
L3= length from the mass
m= mass of beam
I=moment of the beam about its pivot
Taking x1/L1 = x2/L2 = x3/L3
Gives the equations
X1+X2 [CL3^2/(ML1^2+I)] + X1[kL3^2/(ML1^2+I)] = 0
X1+ 2PwnX1 + wn^2 X1 = 0
Wn= natural frequency
P= the damping ratio
A displacement of the beam is monitored from a point L2 from
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