GATE ME 2018 Set 2 — Question 17
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Theory of Machines & Vibrations → Forced Vibration → Damped Free Vibration
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Question
In a single degree of freedom underdamped spring-mass-damper system as shown in the figure, an additional damper is added in parallel such that the system still remains underdamped. Which one of the following statements is ALWAYS true?
Correct answer
(C) Time period of free oscillations will increase.
Solution
For a single degree of freedom underdamped system, the damped natural frequency is given by:where is the undamped natural frequency and is the damping ratio.When an additional damper is added in parallel, the equivalent damping coefficient increases (). Since the mass and stiffness remain constant, the damping ratio increases.As increases (while remaining for an underdamped system), the term decreases. Consequently, the damped natural frequency decreases.The time period of free oscillations is . Since decreases, must increase.Transmissibility () depends on the frequency ratio . The effect of increasing on depends on whether or . Thus, statements (A) and (B) are not always true.Therefore, the time period of free oscillations will always increase.
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