GATE ME 2023 Set 1 — Question 30
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Theory of Machines & Vibrations → Free Vibration → Undamped Free Vibration
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Question
The figure shows a block of mass attached to a pair of identical linear springs, each having a spring constant . The block oscillates on a frictionless horizontal surface. Assuming free vibrations, the time taken by the block to complete ten oscillations is _________ seconds. (Rounded off to two decimal places)Take .
Correct answer
6.27 to 6.29
Solution
Given:
Mass of the block,
Spring constant of each spring,
Number of oscillations, The two springs are connected in parallel as they share the same displacement. Therefore, the equivalent spring constant () is:The natural frequency of the system is:The time period for one oscillation is:The time taken for ten oscillations is:Thus, the time taken is seconds.
Mass of the block,
Spring constant of each spring,
Number of oscillations, The two springs are connected in parallel as they share the same displacement. Therefore, the equivalent spring constant () is:The natural frequency of the system is:The time period for one oscillation is:The time taken for ten oscillations is:Thus, the time taken is seconds.
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