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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 = 200 GPa. If the lateral vibration of this system is critically damped using a viscous damper, the damping constant of the damper is
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- 1250 Ns/m
- 625 Ns/m
- 312.50 Ns/m
- 156.25 Ns/m
Correct Option: A
Given length of cantilever beam,
l = 1000 mm = 1 m
Moment of inertia of the shaft,
| I = | bd3 = | |||
| 12 | 12 |
= 3.25 × 10-8 m4
Esteel = 200 × 109 Pa.
Mass, M = 20 kg
∴ Weight W = 20 × 9.81 = 196.2
Now, deflection of free end,
| δ = | = | = 0.01 m | ||
| 3EI | 3 × 200 × 109 × 3.25 × 10-8 |
As the system is critically damped,
 |  | 2 | = ωn2 | 2m |
Critical damping constant,
Cc = 2mωn = 2 × 20 × 31.22
= 1248.99 N-s/m2.
