The equation of motion of a spring-mass-damper system is given by {d^{2} x}/{d t^{2}}+3 \frac{d x}{d t}+9 x=10 \sin (5 t) . The damping factor for the system is

GATE Mechanical Engineering (ME) 2020 Shift 2 Solved Paper

Question : 33 of 65

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The equation of motion of a spring-mass-damper system is given by

\;{d^{2} x}/{d t^{2}}+3 \;{d x}/{d t}+9 x=10 \sin (5 t) .

The damping factor for the system is

Solution:

\;{ {d}^{2} {x}}/{ {dt}^{2}}+3 \;{ {d} {x}}/{ {dt}}+9 {x}=10 \sin (5 {t})

Damping factor

(ξ)=?

{k}=9, {c}=3, {m}=1

{c}=2 ξ √{ {km}}

3=2 ξ √{1 × 9}

ξ=\;{3}/{6}=0.5

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