GATE Civil Engineering (CE) 2019 Shift 1 Solved Paper

Question : 30 of 65

Marks: +1, -0

A simple mass-spring oscillatory system consists of a mass

{m}

, suspended from a spring of stiffness

{k}

. Considering

{z}

as the displacement of the system at any time

{t}

, the equation of motion for the free vibration of the system is

{mz}+ {kz}=0

. The natural frequency of the system is

Solution:

For simple harmonic motion

m z+k z=0

z+\;{k}/{m} z=0

\;{d^{8} x}/{d^{2}}+w^{2} x=0

Standard equation is

⇒ \; w^{2}=\;{k}/{m}

⇒ \;w=√{\;{k}/{m}}

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