GATE ME 2014 Set 2 — Question 44
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Theory of Machines & Vibrations → Free Vibration → SDOF Free Vibration
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Question
What is the natural frequency of the spring mass system shown below? The contact between the block and the inclined plane is frictionless. The mass of the block is denoted by and the spring constants are denoted by and as shown below.
Correct answer
(D) √((k₁ + k₂)/(m))
Solution
In the given spring-mass system, when the mass is displaced by a distance along the incline, both springs experience the same displacement . One spring is compressed while the other is stretched, but both exert restoring forces in the same direction. Therefore, the springs are in parallel. The equivalent spring constant is . The natural frequency of the system is given by .
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