Torsional pendulum: frequency of oscillation formula Let I be the mass moment of inertia of the suspended body and C be the torsional constant (restoring couple per radian). Select the correct expression for the frequency of oscillation f.
Mechanical Engineering
Engineering Mechanics
Difficulty: Easy
Choose an option
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Af = (1 / 2π) × √(C / I)
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Bf = (1 / 2π) × √(I / C)
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Cf = (1 / 2π) × √(g / L)
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Df = (1 / 2π) × √(C × I)
Answer
Correct Answer: f = (1 / 2π) × √(C / I)
Explanation
Given data
- Torsional pendulum with torsional constant C and moment of inertia I.
Concept/Approach
- Equation of motion: restoring couple = C × angular displacement. This is simple harmonic motion with angular frequency ω such that ω2 = C / I.
Step-by-step relationω = √(C / I)f = ω / (2π) = (1 / 2π) × √(C / I)
Common pitfalls
- Using the simple pendulum formula √(g/L), which does not apply to torsional oscillations.
Final Answerf = (1 / 2π) × √(C / I)