A mechanical machine tool has a mass of m = 500 kg and a mass moment of inertia of J, = 150 kg m² about the centre of gravity. The machine is supported by two clastic supports, the springs have an effective spring constant of k = 150 kN/m and kz = 100 kN/m. The centre of gravity, G located is situated between the two springs with distances l = 0.5 m and lz = 0.8 m as shown in Figure 4.1. 4.1. Compute the cquation of motion for the system in terms of x and 0; and 4.2. Determine the two natural frequencies.

Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
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A mechanical machine tool has a mass of m = 500 kg and a mass moment of inertia of J, =
150 kg · m² about the centre of gravity. The machine is supported by two elastic supports,
the springs have an effective spring constant of k1 = 150 kN/m and kz = 100 kN/m. The
centre of gravity, G located is situated between the two springs with distances l4 = 0.5 m and
z = 0.8 m as shown in Figure 4.1.
4.1. Compute the equation of motion for the system in terms of x and e; and
4.2. Determine the two natural frequencies.
•G
k:
k2
x(t) +
Figure 4.1 Machine tool
Transcribed Image Text:A mechanical machine tool has a mass of m = 500 kg and a mass moment of inertia of J, = 150 kg · m² about the centre of gravity. The machine is supported by two elastic supports, the springs have an effective spring constant of k1 = 150 kN/m and kz = 100 kN/m. The centre of gravity, G located is situated between the two springs with distances l4 = 0.5 m and z = 0.8 m as shown in Figure 4.1. 4.1. Compute the equation of motion for the system in terms of x and e; and 4.2. Determine the two natural frequencies. •G k: k2 x(t) + Figure 4.1 Machine tool
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