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The disc of a torsional pendulum has a mass moment of inertia of $0.06 \ kgm^2$. The brass shaft attached to it is of 100 mm diagram and 400 mm long.
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When the pendulum is vibrating, the observed amplitudes on the same side of the rest position for successive cycles are 9˚, 6˚ and 4˚.

Find:

1] Logarithmic decrement.

2] Damping torque at unit velocity.

3] Periodic time of vibration. Assume the modulus of rigidity $4.4 \times 10^{10} \ N/m^2$

What …

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