A mass M, of 20 kg is attached to the free end of a steel cantilever beam of length 1000 mm having a cross-section of 25 andtimes; 25 mm. Assume the mass of the cantilever to be negligible and Esteel = 200GPa. If the lateral vibration of this system is critically damped using a viscous damper, the damping constant of the damper isa)1250 Ns/mb)625 Ns/mc)312.50 Ns/md)156.25 Ns/mCorrect answer is option 'A'. Can you explain this answer?

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A mass M, of 20 kg is attached to the free end of a steel cantilever beam of length 1000 mm having a cross-section of 25 × 25 mm. Assume the mass of the cantilever to be negligible and E_steel = 200GPa. If the lateral vibration of this system is critically damped using a viscous damper, the damping constant of the damper is

a)
1250 Ns/m
b)
625 Ns/m
c)
312.50 Ns/m
d)
156.25 Ns/m

Correct answer is option 'A'. Can you explain this answer?

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A mass M, of 20 kg is attached to the free end of a steel cantilever b...

Given M = 20kg,I = 1000mm = 1m, A = 25 × 25

mm²

E_Steel = 200GPa = 200 × 10⁹Pa

Mass moment of inertia of a square section is given by,

Deflection of a cantilever, Loaded with a point load placed at the free end is

Therefore, critical damping constant C₀ = 2Mω_n = 2 × 20 × 31.32

= 1252.8Ns/m ≃ 1250Ns/m

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A mass M, of 20 kg is attached to the free end of a steel cantilever beam of length 1000 mm having a cross-section of 25 × 25 mm. Assume the mass of the cantilever to be negligible and Esteel = 200GPa. If the lateral vibration of this system is critically damped using a viscous damper, the damping constant of the damper isa)1250 Ns/mb)625 Ns/mc)312.50 Ns/md)156.25 Ns/mCorrect answer is option 'A'. Can you explain this answer?

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