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In a vibrating system the spring has stiffness 32 N/m and the mass 2 kg. The system is having a damper whose coefficient of viscous damping is 8 N-s/m. The system is:

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  1. Over damped system
  2. Under damped system
  3. Critical damped system
  4. Undamped system

Answer (Detailed Solution Below)

Option 2 : Under damped system
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Detailed Solution

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Concept:

Damping ratio:

ξ > 1: Overdamped system

ξ = 1: Critically damped system

ξ < 1: Under-damped system

Differential equations of damped free vibration

Calculation:

2ẍ + 8ẋ + 32x = 0

On comparing with: mẍ + cẋ + kx = 0

M = 2 kg, c = 8 Ns/m, k = 32 N/m

Damping factor,

∵ ξ < 1, the system is underdamped.

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