A damped harmonic oscillator has a first amplitude of 30 cm. The amplitude reduces to 3 cm after 100 oscillations. If the period of damping is 9.2s calculate the logarithmic decrement and damping factor. Also determine the number of oscillations in which the amplitude drops by 50 percent.

To find the logarithmic decrement (δ) and damping factor (ζ) of the damped harmonic oscillator, we use the formula:

\[ δ = \frac{1}{n} \ln\left(\frac{A_1}{A_n}\right) \]

Where:
- \( A_1 \) is the initial amplitude (30 cm).
- \( A_n \) is the amplitude after a certain number of oscillations (3 cm after 100 oscillations).
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