GATE ME 2017 Set 2 — Question 31
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Theory of Machines & Vibrations → Free Vibration → Undamped Free Vibration
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Question
The radius of gyration of a compound pendulum about the point of suspension is . The distance between the point of suspension and the centre of mass is . Considering the acceleration due to gravity as , the natural frequency (in radian/s) of the compound pendulum is ________
Correct answer
15 to 16
Solution
The natural frequency of a compound pendulum is given by the formula:where:
= mass of the pendulum
= acceleration due to gravity =
= distance from the point of suspension to the centre of mass =
= mass moment of inertia about the point of suspension =
= radius of gyration about the point of suspension = Substituting the expressions:The value rounded to the nearest integer is 16, and it falls within the range 15 to 16.
= mass of the pendulum
= acceleration due to gravity =
= distance from the point of suspension to the centre of mass =
= mass moment of inertia about the point of suspension =
= radius of gyration about the point of suspension = Substituting the expressions:The value rounded to the nearest integer is 16, and it falls within the range 15 to 16.
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