Question
Download Solution PDFIn 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:
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept:
Damping ratio:
\(\xi = \frac{C}{{{C_c}}}\)
ξ > 1: Overdamped system
ξ = 1: Critically damped system
ξ < 1: Under-damped system
Differential equations of damped free vibration
\(m\ddot x + c\dot x + kx = 0\)
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,\(\xi = {\rm{\;}}\frac{{\rm{c}}}{{2\sqrt {{\rm{km}}} }} = {\rm{\;}}\frac{8}{{2\sqrt {32 \times 2} }} = \frac{8}{{2{\rm{\;}} \times {\rm{\;}}8}} = 0.5\)
∵ ξ < 1, the system is underdamped.
Last updated on Jul 2, 2025
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