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A damped pendulum has a time period of 1 s and is continuously losing energy. At one instant, its energy is 45 J. After it has executed 15 complete oscillations, its energy falls to 15 J. The damping constant (in s⁻¹) is:
- 1/2
- 1/30 ln3
- 2
- 1/15 ln3
Correct answer: 1/15 ln3
Solution
The damping constant can be determined using the relationship between the initial and final energy of the damped pendulum over a certain number of oscillations. The formula for energy decay in a damped system shows that the energy decreases exponentially, and by applying this to the given energies and oscillations, we find that the damping constant is correctly calculated as 1/15 ln3.
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