GATE & PSUs - Mechanical Engineering (ME)

Free, Damped & Forced Vibrations (Single DOF) question bank (Theory of Machines & Vibrations)

Practice 7 free GATE & PSUs - Mechanical Engineering (ME) Theory of Machines & Vibrations - Free, Damped & Forced Vibrations (Single DOF) questions with answers and step-by-step solutions.

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Q1.
[Free, Damped & Forced Vibrations (Single DOF) Concept 4] A spring-mass-damper system has mass $m = 10\text{ kg}$, spring stiffness $k = 4000\text{ N/m}$, and damping coefficient $c = 80\text{ N}\cdot\text{s/m}$. What is the damping ratio $\zeta$ and nature of damping?

(A)
$\zeta = 0.20$ (Underdamped)
(B)
$\zeta = 1.00$ (Critically damped)
(C)
$\zeta = 2.00$ (Overdamped)
(D)
$\zeta = 0.05$ (Undamped)
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Q2.
[Free, Damped & Forced Vibrations (Single DOF) Concept 9] A spring-mass-damper system has mass $m = 10\text{ kg}$, spring stiffness $k = 4000\text{ N/m}$, and damping coefficient $c = 80\text{ N}\cdot\text{s/m}$. What is the damping ratio $\zeta$ and nature of damping?

(A)
$\zeta = 0.20$ (Underdamped)
(B)
$\zeta = 1.00$ (Critically damped)
(C)
$\zeta = 2.00$ (Overdamped)
(D)
$\zeta = 0.05$ (Undamped)
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