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.

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 relation
ω = √(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 Answer
f = (1 / 2π) × √(C / I)