Question

On a spring mass damper system the amplitude decays to half the original value in two complete cycles the damping in the system as a percentage of critical damping is

• A. 2.4%
• B. 10%
• C. 5.5%
• D. 7.5%

Answer 1

The correct option is C 5.5%

$\frac{x_1}{x_2}=e^{\xi {\omega }_n{T}_D}=e^{\delta }$

$\frac{x_1}{x_3}=2=e^{\delta }$

$2\delta =ln2$

$\delta =0.3365$

$\frac{2\pi \xi }{\sqrt{1-{\xi }^2}}=0.3465$

From above equation we get,

$\xi =0.055=5.5\%$
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