Question
Download Solution PDFThe equation of motion for a single degree of freedom system is
4ẍ + 9ẋ + 16x = 0
The critical damping coefficient for the system isAnswer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept:
Equation of motion for a single degree of freedom system with one damper is given by
\(m\ddot x + c\dot x + kx = 0\)
Critical damping coefficient, cc = 2ζmωn
\({c_c} = 2ζ m\sqrt {\frac{k}{m}} = 2ζ\sqrt {km}\)
Calculation:
Given:
ζ = 1 (for critically damped)
The equation of motion for a single degree of freedom system is
4ẍ + 9ẋ + 16x = 0
Comparing it with the equation of motion
\(m\ddot x + c\dot x + kx = 0\)
m = 4 kg, c = 9 N/m/s, k = 16 N/m
\(c_c=2\zeta \sqrt {km} = 2\;\sqrt {16 \times 4} = 16~kg/s\)
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