77777 Aluminum 1 mm diameter 35 cm Beam -Aluminum I=3.5 x 10-8 m4 Cable 30 kg Figure Q1(a) 30 cm 2.5 x 10³ N/m

Elements Of Electromagnetics
7th Edition
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Author:Sadiku, Matthew N. O.
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77777
Aluminum
1 mm diameter
35 cm
Beam
-Aluminum
I=3.5 x 10-8 m4
Cable
30 kg
Figure Q1(a)
30 cm
2.5 x 105 N/m
Transcribed Image Text:77777 Aluminum 1 mm diameter 35 cm Beam -Aluminum I=3.5 x 10-8 m4 Cable 30 kg Figure Q1(a) 30 cm 2.5 x 105 N/m
Q1 (a) A mass of 30 kg (shown in Figure Q1(a)) is hung by a spring with stiffness, k = 2.5
x 105 N/m, which is attached to an aluminum beam (E = 71 x 10° N/m², p = 2.7 x
10³ kg/m³) with moment of inertia, I = 3.5 x 108 m4 and length 35 cm. The beam is
supported at its free end and by a circular aluminum cable of diameter 1 mm and
length 30 cm. Identify the equivalent of the assembly and describe the differential
equation governing the motion of the mass (assuming the beam and cable are
massless).
Stiffness equation of beam is k
EA
L
=
3EI
and stiffness equivalent of the cable is kc =
L3
Transcribed Image Text:Q1 (a) A mass of 30 kg (shown in Figure Q1(a)) is hung by a spring with stiffness, k = 2.5 x 105 N/m, which is attached to an aluminum beam (E = 71 x 10° N/m², p = 2.7 x 10³ kg/m³) with moment of inertia, I = 3.5 x 108 m4 and length 35 cm. The beam is supported at its free end and by a circular aluminum cable of diameter 1 mm and length 30 cm. Identify the equivalent of the assembly and describe the differential equation governing the motion of the mass (assuming the beam and cable are massless). Stiffness equation of beam is k EA L = 3EI and stiffness equivalent of the cable is kc = L3
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